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Volume 2 

Issue 2 

ISSN: 2161-7155 

Journal of Engineering and Technology 

October, 2012

TABLE OF CONTENTS 

Table of Contents 

PARAMETRIC STUDY OF SANDWICH PANEL BUCKLING IN COMPOSITE WIND TURBINE 

BLADES 

Shicong Miao, Steven Donaldson, Elias Toubia……………………………………………………………………….….……3 

A STUDY OF SIMPLIFIED SHALLOW WATER WAVES: ASSESSMENT OF ADOMIAN’S 

DECOMPOSITION METHOD FOR THE ANALYTICAL SOLUTION 

Mehdi Safari……………………………………………………………………………………….……………………..….…….16 

ON BICRITERIA LARGE SCALE TRANSSHIPMENT PROBLEMS 

Dr. Jasem M.S. Alrajhi, Dr. Hilal A. Abdelwali, Dr. Mohsen S. Alardhi, Eng. Rafik El Shiaty…….…………..…..….21 

TRIBOLOGY OF HIGH SPEED MOVING MECHANICAL SYSTEMS FOR SPACECRAFTS - 

TRIBOLOGICAL ISSUES 

K. Sathyan……………………………………………………………………………………………………..…………..……....27 

THE USE OF IRON IN PEAT WATER FOR FENTON PROCESS 

Mirna Apriani, Ali Masduqi……………………………………………………………………………………..……….……..35 

TRIBOLOGY OF HIGH-SPEED MOVING MECHANICAL SYSTEMS FOR SPACECRAFTS: 

LUBRICATION SYSTEMS OF BALL BEARINGS 

K. Sathyan………………………………………………………………………………………………………………………..39 

AcademyPublish.org – Journal of Engineering and Technology Vol.2, No.2 2

PARAMETRIC STUDY OF SANDWICH PANEL BUCKLING IN COMPOSITE WIND TURBINE BLADES 

Shicong Miao, Steven Donaldson, and Elias Toubia 

Parametric Study of Sandwich Panel Buckling in Composite Wind Turbine Blades 

Shicong Miao, Steven Donaldson * , and Elias Toubia 

*Corresponding author: steven.donaldson@notes.udayton.edu 

Department of Civil and Environmental Engineering, University of Dayton, Dayton, OH 45469. USA 

ABSTRACT: A parametric study of the buckling performance of composite wind turbine blade regions with thin symmetric laminated sandwich 

rectangular panels, subjected to uniform axial shell edge compression loads is presented. The research focused on the critical buckling load and strain 

levels with core material parameters, such as transverse core shear modulus and core thickness, for rectangular sandwich strips with long aspect ratios. 

Both flat and curved-section models were considered. The buckling design plots generated provide an insight into optimal core solutions for efficient 

designs. 

NOMENCLATURE 

a = length of the panel, m 

b = width of the panel, m 

c = core thickness, m 

k = panel curvature ratio, % (arc height divided by the panel width) 

l = curve length, m 

r = radius, m 

t = facing thickness on one surface, m 

h = overall thickness of sandwich 

C 0 = normalized core thickness (core thickness divided by total facing 

sheet thickness) 

1, 2, 3 = general coordinates. (1:longitudinal direction; 2: width 

direction; 3: direction normal to the panel planform) 

r, t, z = cylindrical coordinates. (r: radial direction normal to panel; t: 

curve angle direction; z: longitudinal direction) 

U 1, U 2 , U 3 = displacement in 1, 2, 3 direction 

U r, U z , U t = displacement in r, z, t direction 

P cr = critical buckling end load (=eigenvalue), N/m 

ε cr = critical buckling end strain, % 

E 1 , E 2 , E 3 = Moduli of elasticity 

G 13 = Core transverse shear modulus in 1-3 plane, Pa 

G 23 = Core transverse shear modulus in 2-3 plane, Pa 

ν 12 , ν 21, ν 23 = Poisson's ratios 

N 1 = Uniform compressive end load, N/m 

INTRODUCTION 

Renewable energy sources continue to increase as a percentage of 

global energy production. This trend is dominated by wind energy and 

is the result of both an increase in the number of turbines installed, as 

well as the increasing diameter of turbine rotors with the corresponding 

energy output per turbine (Roczek, 2010). As a consequence of this 

design strategy, the blade structures are becoming increasingly thinwalled, 

such that buckling problems in the blade panels must be 

addressed (Lund, Johansen, 2008). 

In general, the wind turbine blade works in much the same way as the 

steel I-beam, except that there are shells around the outside that form 

the aerodynamic shape and resist buckling and torsional loads (WE 

Handbook- 3- Structural Design). Utility-scale wind turbine blades use 

extensive sandwich construction, in both the aerodynamic shells and 

shear webs. To meet stiffness constraints such as deflection limits, the 

fiber composite materials in the broad unsupported spans of shell and 

shear web laminates are stiffened through the use of sandwich 

construction to prevent local deformation and buckling. In blade 

structures, the largest single role of the sandwich core is to assure 

adequate stability of the large panel regions against buckling. As such, 

the most significant attributes of the core materials are the transverse 

shear modulus and the core thickness. Since core materials are 

generally available in a wide range of weights, mechanical properties, 

and cost, a study focused on the shell core is appropriate. 

Several related and valuable plate buckling studies and wind turbine 

blade preliminary design studied have been done in this area. General 

wind turbine blade optimization methods are discussed and presented in 

(Roczek, 2010, Lund, Johansen, 2008 and Lund, 2005). Structural 

reliability and mechanical behavior predictions for blade materials are 

reported in reference (Mishnaevsky et al., 2011). A preliminary design 

study of an advanced 50 m blade for utility wind turbines is presented 

in reference (Jackson et al., 2005) Closed form, exact solutions for the 

buckling of simply supported, rectangular, orthotropic plates under 

different load conditions are given in (Narita, Leissa, 1990, Leissa, 

1985). Many nondimensional buckling parameters were generated by 

Nemeth and Weaver ( Nemeth, 1995, Nemeth 2004, Weaver, Nemeth, 

2007) for long or infinitely long symmetrically laminated anisotropic 

rectangular plates subjected to various combined load conditions. 

Theoretical prediction of buckling loads for cyclic sandwich shells 

under axial compression with laminated facings and foam core is 

presented in (Morovvati, 2011). Although many researchers have 

investigated the buckling of simply supported laminated composite 

plates, the early buckling analysis works focused on anisotropic plate 




excluding sandwich plates or shells. Therefore, it is useful to perform a 

parametric study of both flat and curved section strips representing 

different characteristic regions of sandwich laminates in blades. 

A parametric study of the buckling performance of core materials on 

the basis of transverse shear modulus and thickness, within a given 

design domain (a fixed set of laminate designs and critical buckling 

loads) is presented. This will provide insight into optimal core 

solutions. This study considers both flat and curved-section rectangular 

sandwich strip models with long aspect ratios, which provide close 

approximations to the buckling loads and mode shapes (wavelengths) 

expected in the sandwich panel regions of the blades. Considering the 

design process and the characteristic strains in axial compression 

conditions, the buckling trends are on the basis of both critical buckling 

load and strain. 

A complete parametric study using practical design properties does not 

appear to exist in the literature, and was therefore the goal of this study. 

The results of the present work in practical design optimization studies 

would then involve assessing the cost and weight of various core 

products as an indication of optimal thickness values, then comparing 

the cost and weight of the various solutions. 

ANALYSIS AND DESCRIPTION 

Finite Element Analysis 

In setting up the model, two panel models (flat and curved -section) 

were considered to represent different regions of the blade shell. It was 

assumed that all layers of the panel were perfectly bonded together and 

thus the displacements were continuous throughout the thickness. 

The model of the panel strips were built in ABAQUS 6.10 with 

elements of S4R (ABAQUS User’s Manuals, Version 6.10). For the 

flat-section model, there were a total of 1111 nodes and 1000 elements 

used. The curved section model used 1313 nodes and 1200 elements. 

This mesh density was established in a prior convengence study by 

Toubia (Toubia, 2008). 

The general boundary condidtions of the sandwich panel models are 

shown in Figure 1. In the flat-section model, on the loaded edge, U 2 = 

U 3 = 0. The long edges have U 2 = U 3 = 0, and the far end has U 1 = U 2 = 

U 3 = 0. In the curved-section model, on the loaded edge, U t = U r = 0. 

In this initial study, the load profile was assumed to be uniform across 

the ends (later studies to examine non-uniform loading are appropriate). 

The long edges have U t = U r = 0, and the far end has U t = U r = U z = 0. 

The analyzed material data and panel model information can be found 

in Table 1 and Table 2. The facing material used in this study is E_TLX 

5500 ( E_TLX5500, 15 December 2011.) which is [0/45/-45] E-glass 

material commonly used as composite reinforcement in wind turbine 

blade shell regions. Four representative core materials (M1 to M4) are 

selected to cover the prevalent material shear modulus range. The 

critical buckling eigenvalues were found by buckling analysis using 

ABAQUS, and then applied in the linear analysis approach to obtain 

the critical buckling strains. Sample dominant buckling mode shapes 

are shown in Figure 2 and Figure 3. 

Figure 1. General bounduary conditions of the infinitely long strip of the panel (1, 2, 3) and shell (r, t, z) 




Figure 2. ABAQUS buckling wavelength result for flat-section sandwich panel model 




Figure 3. ABAQUS result for high aspect ratio curved-section sandwich panel model a) with no rigid ends and b) rigid ends included 

Closed Form Solution Validation 

The flat-section model result was validated by the closed form solutions 

provided by Allen(Allen, 1969) for orthotropic sandwich panels(valid 

for flat plates only). The infinitely long curved plate solution for 

isotropic plates was found in Gambhir (Gambhir, 2004). 

Since the S4R element in ABAQUS is a soft shell element, rigid ends 

were required in the sandwich panel models to get more accurate 

buckling eigenvalues. The validated results can be seen in Figure 4. 

The core transverse shear moduli, G 13 and G 23 , are studied because they 

are the core properties that have the most significant effect on panel 

buckling (Toubia, 2008). As shown in Figure 4, for a core with high 

transverse shear modulus G 13 , the FEA result and analytical solutions 

converge. When the core shear modulus is too low, the local skin 

buckling wrinkling mode is dominant. As shown in Table 1, the lowest 

shear modulus studied has a value of G 13 of 20 MPa (less than a 5% 

deviation from the closed form solution), while the highest had a value 

of 250 (essentially no deviation). 




Figure 4. Flat model FEA result compare with the closed form solution 

RESULTS AND DISCUSSION 

Critical Buckling Load Nx*10 9 

(N/m) 

FEA compare with closed form solution 

1200 

1100 

1000 

900 

800 

700 

600 

500 

The local buckling phenomenon, such as core shear crimping and skin 

wrinkling, are discussed in references (Eringen, 1952, Vinson, 1999). 

The core thickness and shear modulus must be adequate to prevent the 

panel from buckling or failing under end compression loads. The 

compressive modulus of the facing skin and the core compression 

strength must both be high enough to prevent a skin wrinkling failure. 

Since the anayzed skin material is sufficently stiff, local skin failure 

was not taken into consideration herein (Toubia, 2008). Each of the 

curves in the subsequent plots were created from five or six individual 

calculation points. Since no dramatic shape variations were observed 

in the results, for clarity the individual data points are not shown, but 

smoothed lines are presented. 

0 20 40 60 80 100 120 

G 13 (MPa) 

FEA S4R 

ANALYTIC 

AL 

Flat Panel Core Thickness Study 

Figure 5 shows the effects of increasing the core transverse shear 

modulus (M1 through M4), increasing the number of facing layers (1 

layer facing to 5), and increasing the core thickness (C 0 is the core 

thickness divided by the facing thickness) on the critical buckling load, 

N 1 . Figure 5 illustrates that a higher transverse shear modulus increases 

critical buckling load. It is also clear that both increasing the number of 

facing layers, as well as increasing the core thickness lead to increases 

in the critical buckling load. Note that while increasing the thickness of 

the core, the critical buckling loads increase faster in the cases with 

higher transverse core shear modulus. Also, for increased core 

thickness, a higher number of layer facing results in rapid increases in 

critical buckling load. Figure 6 depicts similar trends for the laminate 

critical strain values: transverse shear modulus of the core, core 

thickness, and number of facing layers are the dominant aspects in 

sandwich panel buckling resistance. 

Figure 5. Critical buckling load versus normalized core thickness C 0 for all five facing layers and all four core materials. Flat-section. 1m width 

sandwich panel. 

Critical Buckling Load N 1 *10 5 (N/m) 

45 

40 

35 

30 

25 

20 

15 

10 

5 

0 

1 3 5 7 9 11 13 15 

Normalized core thickness C 0 




Figure 6. Critical buckling strain versus core thickness for all five facing layers and all four core materials. Flat-section. 1m width sandwich panel. 

Note that the strain is dependent on N cr /2t (assuming half of the load is 

carried by top and bottom skin, t is the thickness of each the skin, N cr is 

N/m per linear width b). For a low modulus core, core shear instability 

(shear crimping) governs the buckling load. The shear modulus is not 

stiff enough to engage the top and bottom skin. So if we look at the 

formula: cr =G*h/(2t) ( core shear instability formula for isotropic 

core), and = (str ain, )*E, and = (Ncr/2(b t))= (strain, )*E, then 

N cr /2t decreases as strain decreases. Since N cr increases as the skin 

thickness increases, N cr is divided by the number of plies, this number 

decreases for the low modulus core. As for the stiffer core, the shear 

modulus is high enough that the core is coupling and engaging the skins 

to effectively carry the buckling load, therefore global buckling occurs. 

The more the number of plies is increased, the more the structure is 

straining, until an asymptotic line is reached that the buckling cannot go 

beyond, until the shear modulus is increased.Figure 7 separates the 

results by core type (M1-M4). 

Figure 7. Critical buckling strain versus core thickness for core material M1, M2, M3, M4. Flat-section. 1m width sandwich panel 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

20 25 30 35 40 45 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

20 25 30 35 40 45 




0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

20 25 30 35 40 45 

1.2 

1.1 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

20 25 30 35 40 45 

In Figure 8, the width of the panel was increased from 1m to 5m to 

depict the panel width effect. For each core thickness, the upper curve 

is 5 layers, the lowest is 1 layer. Note the critical buckling loads drop 

faster with increasing core shear modulus. The trends level off as the 

width increases to around 3m due to global flexibility. Strain is not 

shown because, for the flat panel, the critical buckling strain is the same 

regardless of panel width. 

Figure 8. Critical buckling load versus panel width for material M1, M2, M3 M4 in 20, 30, 40mm core thickness. Flat-section. 1m, 3m, 5m width 

sandwich panel. For each core thickness, the upper curve is 5 layers, the lowest is 1 layer. 

12 

25 

10 

20 

8 

6 

15 

4 

10 

2 

5 

0 

1 2 3 4 5 

0 

1 2 3 4 5 

30 

35 

25 

20 

15 

30 

25 

20 

15 

10 

10 

5 

5 

0 

1 2 3 4 5 

0 

1 2 3 4 5 

To gain insight into the critical buckling strain versus core transverse 

shear modulus relationship, additional hypothetical core materials (see 

Table 3) are introduced in Figure 9. Note core material M3 is an 

unbalanced core with a shear modulus G 13 =108 Mpa and G 23 =72 Mpa. 

All other core materials are balanced (G 13 = G 23 ). Compared with core 

material Q1, M3 has an 8% increase in G 13 and 28% decrease in G 23 , 




the result is approximately 9.6% maximum decrease in buckling strain. 

For core material Q5, the shear modulus is the same as Q4 but up to 

28.6% decrease in material elastic modulus. The result is only 

maximum 3.3% decreased in buckling strain. The results indicate that 

in sandwich buckling resistance, the core transverse shear modulus is a 

major characteristic aspect, while the material elastic modulus has 

negligible effect on the critical strain level.The trends are almost 

constant when the core shear modulus increases. Critical buckling 

strains are proportional with the increase in core thickness. As such, 

core thickness is another major aspect in sandwich buckling 

resistance.The results are expanded in Figure 10 to include additional 

face sheet layer combinations. 

Figure 9. Critical buckling strain versus core transverse shear modulus in 20, 30, 40mm core. 1 facing layer. Flat-section sandwich panel. 

Critical buckling strain ε (%) 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

M 

1 

M 

1 

M 

1 

M 

2 

M 

2 

M 

2 

Q1 

Q1 

Q1 

1 facing 

M 

M 

M 

20 40 60 80 100 120 140 160 180 200 220 240 

Transverse shear modulus 

Q5 

Q2 Q3 Q4 

Q3 

Q3 

Q5 

Q4 

Q5 

Q4 

M 

4 

M 

4 

M 

4 

40m 

30mm 

20mm 

Figure 10. Critical buckling strain versus core transverse shear modulus in 20, 30, 40mm core. All 5 facing layers. Flat panel. 1m width 


1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

40mm 

30mm 

20mm 

5 layer 

4 layer 

3 layer 

2 layer 

1 layer 

5 layer 

4 layer 

3 layer 

2 layer 

1 layer 

5 layer 

4 layer 

3 layer 

2 layer 

1 layer 

0.1 

0 

20 70 120 170 220 

Transverse shear modulus (Mpa) 




Curved Panel Curvature Ratio and Core Thickness Study 

In the curved-section sandwich panel models (see Figure 11), the 

results clearly indicate that the buckling loads increase quickly with 

curvature of the plate, core thickness, and number of facing layers. It is 

also shown that the ‘critical curvature ratio’ exists for a fixed core 

material and thickness, where the trends of the critical buckling loads 

reach a high point and then level off. Local buckling occurs after that. 

For the lower shear modulus core materials, the ‘critical curvature 

ratio’ occurs earlier than those with high shear modulus. In the practical 

design, it reveals those sandwich panels made of lower shear modulus 

core materials are not suitable to be made with large curvature ratio to 

resist buckling. Alternatively, when the core shear modulus is high, the 

trend is still upward (no critical point is reached). 

For the critical buckling strains in the curved-section panel models 

(Figure 12), the plots show that the strains decrease and then increase 

as the curvature of the plate increases. The results of variations in the 

transverse shear modulus in curved-section sandwich panel models are 

shown in Figure 13. The critical buckling strain increases when the 

core thickness and section curvature ratio increases 

Figure 11. Critical buckling load versus panel curvature ratio for core material M1, M2, M3, M4 in 20, 30, 40mm core thickness and all five facing 

layers. Curved-section panel. 

14 

30 

12 

10 

8 

6 

25 

20 

15 

4 

10 

2 

5 

0 

0 5 10 15 20 25 

0 

0 5 10 15 20 25 

45 

140 

40 

35 

30 

25 

20 

15 

10 

5 

0 

0 5 10 15 20 25 

120 

100 

80 

60 

40 

20 

0 

0 5 10 15 20 25 




Figure 12. Critical buckling strain versus panel curvature ratio for core material M1, M2, M3, M4 in 20, 30, 40mm core thickness and all five facing 

layers. Curved-section panel. 

0.7 

1.2 

0.6 

1 

0.5 

0.4 

0.3 

0.2 

0.8 

0.6 

0.4 

0.1 

0.2 

0 

0 10 20 

0 

0 5 10 15 20 25 

1.4 

1.6 

1.2 

1.4 

1 

0.8 

0.6 

0.4 

0.2 

0 

0 5 10 15 20 25 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

0 5 10 15 20 25 




Figure 13. Critical buckling strain versus transverse shear modulus in 5%, 10%, 25% curvature, 20mm core, Curved panel, all 5 layers. 


1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

20mm Core 

25% 

10% 

5% 

20 70 120 170 220 

Transverse shear modulus (Mpa) 

5 layer 

4 layer 

3layer 

2 layer 

5 layer 

4 layer 

3layer 

2 layer 

1 layer 

5 layer 

4 layer 

3layer 

2 layer 

1 layer 

PRELIMINARY DESIGN EXAMPLE 

Figure 14 shows a repeat of Figure 6 to be used as a design example. 

In this example, the critical buckling design strain has been previously 

chosen based on other factors ( maximum blade deflection, joining, 

damage tolerance, etc.), and required to be equal to or greater than 

0.5%. Several combinations of core selection, core thickness, and 

facing thickness are depicted in Figure 14 (only three are shown of a 

possible 12 curve intersections): 

A. approximately 27mm thickness of core M4 with 5 facing layers; 

B. approximately 33mm thickness of core M3 with 1 facing layers; 

C. approximately 41mm thickness of core M4 with 2 facing layers; 

Based on the cost and weight of facing materials and core materials, the 

optimal choice can be made to minimize or balance the cost and the 

weight of the structure. 

Figure 14. Critical buckling strain versus core thickness for all five facing layers and all four core materials. Flat-section. 1m width sandwich panel. 

Critical buckling strain ε 

1.2 

1 

0.8 

0.6 

0.5 

0.4 

0.2 

M 

1 

M 

2 

b=1m 

A B 

0 

20 25 30 35 40 45 

Core thickness 

5 

layer 

4 

layer 

1 layer 

2 layer 

3 layer 

4 layer 

5 layer 




CONCLUSIONS 

A finite element based study of the buckling of composite sandwich 

panels (as seen in wind turbine blade shells) was conducted to examine 

the sensitivity of critical buckling load and strain levels to multiple 

design parameters, including the core transverse modulus, core 

thickness, number of facing layers, panel width, and panel curvature. 

The results of this project provide a more efficient preliminary design 

method to assess sandwich panel buckling in wind turbine blade design. 

The results from this study in practical design optimization would 

involve assessing the variables listed above, then comparing the cost 

and weight of the various solutions toward the design objectives such 

as minimizing cost or weight. 

ACKNOWLEDGEMENT 

The discussions with Fred Stoll of Milliken & Co. are gratefully 

appreciated. 

REFERENCES 

ABAQUS User’s Manuals, Version 6.10 ( Volume I-III, Hibbitt: 

Karlson and Sorensen, Inc., Pawtucket, RI.) 

Allen HG. Analysis and design of structural sandwich panels. 

Pergamon Press, Oxford 1969. 

E_TLX5500. http://www.vectorply.com/pdf/e-tlx%205500.pdf. 

Accessed 15 December 2011. 

Eringen AC. Bending and buckling of rectangular plates. Proceedings 

of the first U.S. National congress of applied mechanics, ASME, New 

York 1952. 381-390. 

Gambhir ML. Stability analysis and design of structure. Springer 2004. 

http://proquest.umi.com/pqdlink?did=1537815401&Fmt=7&clientI%2 

0d=79356&RQT=309&VName=PQD. Accessed 15 December 2011. 

http://www.gurit.com/files/documents/3_Blade_Structure.pdf 

Jackson, K, Zuteck, M, van Dam, C, Standish, ., Berry, D. Innovative 

Design Approaches for Large Wind Turbine Blades. Wind Energy 

2005; 8:141–171. 

Leissa AW. Buckling of laminated composite plates and shell panels. 

Air Force Wright Aeronautical Laboratories 1985, Final Report, No. 

AFWAL-TR-85-3069. 

Lund E, Johansen LS, On Buckling Optimization of a Wind Turbine 

Blade. Mechanical Response of Composites, Computational Methods in 

Applied Sciences 2008, Volume 10, 243-260. 

Lund E. On Structural Optimization of Composite Shell Structures 

Using a Discrete Constitutive Parametrization. Wind Energy 2005; 

8:109–124. 

Mishnaevsky, L., Brøndsted, P., Nijssen, R., Lekou, D. and Philippidis, 

T. Materials of large wind turbine blades: recent results in testing and 

modeling. Wind Energy 2011. 

Morovvati MR. Buckling of Generally Anisotropic Sandwich Shells. 

American Society of Composites 26th Annual Technical Conference 

2011, 1143. 

Narita Y, Leissa AW. Buckling studies for simply supported 

symmetrically laminated rectangular plates. Int. J. Mech. Science 1990, 

Volume 32, No. 11, 909-924. 

Nemeth MP. Buckling Behavior of Long Anisotropic Plates Subjected 

to Combined Loads. National Aeronautics and Space Administration 

Langley Research Center 1995, 1-37. 

Nemeth MP. Buckling of long compression-loaded anisotropic plates 

restrained against inplane lateral and shear deformations. Thin-Walled 

Structures 2004. Volume 42 639–685. 

Roczek A. Optimization of trailing edge sandwich panels for a wind 

turbine blade. 9th International Conference on Sandwich Structures 

2010. 

Toubia EA. Web buckling behavior under in-plane compression and 

shear loads for web reinforced composite sandwich core, Ph.D. 

dissertation, University of Dayton 2008, available at: 

Vinson JR. The behavior of sandwich structures of isotropic and 

composite materials. TECHNOMIC Publishing Company, Inc 1999. 

WE Handbook- 3- Structural Design. Available at: 

Weaver PM, Nemeth MP. Bounds on Flexural Properties and Buckling 

Response for Symmetrically Laminated Composite Plates. Journal of 

Engineering Mechanics 2007, 1178-1191 

Table 1: Candidate Material Properties 

Face/Core E 1 E 2 E 3 ν 12 ν 13 ν 23 G 12 G 13 (G 1 ) G 23 (G 2 ) 

MPa MPa MPa MPa MPa Mpa 

E_TLX 5500 21400 10000 0.4 6000 3740 3740 

(face sheet) 

M1 50 50 50 0.33 0.22 0.1 20 20 20 

M2 100 100 100 0.2 0.2 0.2 30 50 50 

M3 284 250 210 0.39 0.25 0 146 108 72 

M4 400 400 400 0.2 0.2 0.2 250 250 250 




Table 2: Panel Model information 

Variables Range Description 

Number of facing layers analyzed 1~5 Increased by 1 

Thickness of each layer (m) 0.0015 Increased by 0.0015 

Range of core thickness (m) 0.02~0.045 Increased by 0.005 

Range of panel width b (m) 1~5 1m, 3m, 5m 

Range of panel curvature ratio (%) 0~25% Flat, 5%, 10%, 25% 

Aspect ratio (length/width; a/b) 5 Constant 

Shell edge load (N/m) 1 Uniformly distributed 

Table 3: Additional Core Material Properties 

Face/Core E 1 E 2 E 3 ν 12 ν 13 ν 23 G 12 G 13 (G 1 ) G 23 (G 2 ) 

MPa MPa MPa MPa MPa Mpa 

Q1 150 150 150 0.2 0.2 0.2 100 100 100 

Q2 200 200 200 0.2 0.2 0.2 120 120 120 

Q3 250 250 250 0.2 0.2 0.2 150 150 150 

Q4 350 350 350 0.2 0.2 0.2 200 200 200 

Q5 250 250 250 0.2 0.2 0.2 200 200 200 


A STUDY OF SIMPLIFIED SHALLOW WATER WAVES: ASSESSMENT OF ADOMIAN’S DECOMPOSITION METHOD 

FOR THE ANALYTICAL SOLUTION 

Mehdi Safari 

A Study of Simplified Shallow Water Waves: Assessment of Adomian’s Decomposition Method for the 

Analytical Solution 

Mehdi Safari, ms_safari2005@yahoo.com 

Department of Mechanical Engineering, Aligoodarz Branch, Islamic Azad University, P. O. Box 159, Aligoodarz, Iran. 

Corresponding author: Tel/Fax: +98 861 3672399 

ABSTRACT 

In this paper, we consider two model equations for shallow water waves. Shallow water waves were introduced as a model equation which reduces to 

the KdV equation in the long small amplitude limit. Large classes of linear and nonlinear differential equations, both ordinary as well as partial, can be 

solved by the ADM.The decomposition method provides an effective procedure for analytical solution of a wide and general class of dynamical 

systems representing real physical problems.This method efficiently works for initial- value or boundary-value problems and for linear or nonlinear, 

ordinary or partial differential equations and even for stochastic systems. Moreover, we have the advantage of a single global method for solving 

ordinary or partial differential equations as well as many types of other equations. We use Adomian’s decomposition method (ADM) to solve them. 

The results show that Adomian's decomposition method is a powerful method for solving these equations and the obtained solutions are shown 

graphically. 

Keywords: Adomian’s decomposition method; Shallow water wave equation 

INTRODUCTION 

Clarkson et.al (Clarkson, Mansfield, 1994) investigated the generalized 

short water wave (GSWW) equation 

u 

t 

uxxt 

uut 

ux utdx 

ux 

0, 

x 

(1) 

where and are non-zero constants. 

Ablowitz et. al. (Ablowitz et al., 1974) studied the specific case 

where Eq. (1) is reduced to 

4 and 2 

t 

uxxt 

4uut 

2u 

x utdx 

ux 

0, 

x 

u (2) 

This equation was introduced as a model equation which reduces to the 

KdV equation in the long small amplitude limit (Ablowitz et al., 1974, 

Hirota, Satsuma, 1976). However, Hirota et.al. (Hirota, Satsuma, 1976) 

examined the model equation for shallow water waves 

t 

uxxt 

3uut 

3u 

x utdx 

ux 

0, 

x 

u (3) 

obtained by substituting 3 in (1). 

Equation (2) can be transformed to the bilinear forms 

 

 

D 

 

( D D D 

D 

1 

) Dt 

( D 

3 

D 

 

) 

 

f . f 

 

0, 

2 

3 

x t t x x 

s x 

(4) 

where s is an auxiliary variable, and f satisfies the bilinear equation 

D ( D 

D 

) f . f 

0, 

3 

x s x 

(5) 

However, Eq.(3) can be transformed to the bilinear form 

D ( D D D 

D 

) f . f 

0, 

2 

x t t x x 

(6) 

and the solution of the equation is 

u x, 

t) 

2(ln f ) , 

(7) 

( 

xx 

where f(x, t) is given by the perturbation expansion 

 

n1 

n 

f ( x, 

t) 

1 

f ( x, 

t), 

(8) 

n 




Mehdi Safari 

here is a bookkeeping non-small parameter, and ( x, 

t) 

f n , n = 1, 

2,…are unknown functions that will be determined by substituting 

the last equation into the bilinear form and solving the resulting 

equations by equating different powers of to zero. 

The customary definition of the Hirota’s bilinear operators are given by 

n m n m 

Dt 

Dx 

a. b ( ) ( ) a( 

x, 

t) 

b( 

x', 

t') | x' 

x, 

t' 

t. 

(9) 

t 

t' 

x 

x' 

Some of the properties of the D-operators are as follows 

2 

Dt 

f . f 

 

2 

f 

Dt 

D 

f 

3 

x 

2 

2 

Dx 

f . f 

2 

f 

4 

Dx 

f . f 

2 

f 

6 

Dx 

f . f 

2 

f 

f . f 

u, 

u 

Dt 

Dx 

f . f 

2 

f 

Where 

 

u 

u dxdx, 

u 

2x 

3u 

ln( f 

4x 

tt 

xt 

3u 

2 

2 

) 

, 

xt 

15uu 

 

, 

2x 

xu dx', 

t 

15u 

3 

, 

(10) 

u x, 

t) 

2(ln f ( x, 

t)) 

, 

(11) 

( 

xx 

Also extended model of Eq.(2) is obtained by the operator 

bilinear forms (4) 

and (5) 

 

 

D 

 

( D D D 

D 

3 1 

Dx 

) Dt 

( Ds 

D 

3 

4 

Dx 

 

) 

 

f . f 0, 

 

to the 

2 

3 

x t t x x 

x 

(12) 

where s is an auxiliary variable, and f satisfies the bilinear equation 

D ( D 

D 

) f . f 

0, 

3 

x s x 

(13) 

Using the properties of the D operators given above, and differentiating 

with respect to x we obtain the extended model for Eq.(2) given by 

t 

x 

u (14) 

uxxt 

4uut 

2u 

x utdx 

ux 

uxxx 

6uux 

0, 

In a like manner, we extend Eq.(3) by adding the operator 

bilinear forms (6) to obtain 

D ( D D D 

D 

D 

) f . f 

0, 

4 

Dx 

to the 

2 

3 

x t t x x x 

(15) 

Using the properties of the D operators given above we obtain the 

extended model for Eq.(3) given by 

t 

x 

u (16) 

uxxt 

3uut 

3u 

x utdx 

ux 

uxxx 

6uu 

x 

0, 

In this paper, we use the Adomian’s decomposition method (ADM) to 

obtain the solution of two considered equations above for shallow water 

waves. Large classes of linear and nonlinear differential equations, both 

ordinary as well as partial, can be solved by the ADM (Adomian, 1991, 

Adomian, Rach, 1991, Adomian 1994, Adomian, 1998, Abbaoui, 

Cherruault, 1999, Kaya, Yokus, 2002, Wazwaz, 2002, Wazwaz, 1997, 

Wazwaz, 2000, Wazwaz 1999, Ganji et al., 2011, Safari et al., 2009). A 

reliable modification of ADM has been done by Wazwaz (Ganji et al., 

2009).The decomposition method provides an effective procedure for 

analytical solution of a wide and general class of dynamical systems 

representing real physical problems (Adomian, 1991, Adomian, Rach, 

1991, Adomian 1994, Adomian, 1998, Abbaoui, Cherruault, 1999, 

Kaya, Yokus, 2002, Wazwaz, 2002, Wazwaz, 1997, Wazwaz, 2000, 

Wazwaz 1999, Ganji et al., 2011).This method efficiently works for 

initial- value or boundary-value problems and for linear or nonlinear, 

ordinary or partial differential equations and even for stochastic 

systems. Moreover, we have the advantage of a single global method 

for solving ordinary or partial differential equations as well as many 

types of other equations. 

BASIC IDEA OF ADOMIAN’S DECOMPOSITION 

METHOD 

We begin with the equation 

Lu R()()() 

u F u g t , (17) 

where L is the operator of the highest-ordered derivatives with respect 

to t and R is the remainder of the linear operator. The nonlinear term is 

represented by F (u). Thus we get 

Lu g ()()() t R u F u , (18) 

The inverse 

L 

1 

t 

t 

1 

L 

dt 

0 

is assumed an integral operator given by 

, (19) 




Mehdi Safari 

The operating with the operator 

1 

0 

(()()()) 

1 

L on both sides of Eq. (18) we have 

u f L g t R u F u , (20) 

where f 

0 

is the solution of homogeneous equation 

Lu 0 , (21) 

involving the constants of integration. The integration constants 

involved in the solution of homogeneous equation ( 21) are to be 

determined by the initial or boundary condition according as the 

problem is initial-value problem or boundary-value problem. 

The ADM assumes that the unknown function u ( x ,) t can be 

expressed by an infinite series of the form 

 

u ( x ,)( t ,) u 

n 

x t , (22) 

n 0 

and the nonlinear operator F () u can be decomposed by an infinite 

series of polynomials given by 

 

F () u An 

, (23) 

n 0 

where u 

n 

( x ,) t will be determined recurrently, and An 

are the socalled 

polynomials of u 

0, u1,..., u 

n 

defined by 

n 

1 d 

An F () , u 0,1, n2... 

 

n 

n ! d 

 

 

 

i 

 

i 

n 0 

0 

(24) 

ADM IMPLEMENT FOR FIRST MODEL OF SHALLOW 

WATER WAVE EQUATION 

We first consider the application of ADM to first model of shallow 

water wave equation. If Eq. (2) is dealt with this method, it is formed as 

L u L u 4uL u 2L u L udx L u, 

(25) 

t 

where 

xxt 

t 

3 

 

 

L t 

, L x 

, L xxt 

, 

2 

t x x 

t 

If the invertible operator 

L 

1 

t 

x 

t 

x 

t 

dt 

0 

x 

(26) 

is applied to Eq. 25, then 

L L u L 

1 

t 

t 

1 

t 

( L 

is obtained. By this 

xxt 

u( 

x, 

t) 

u( 

x,0) 

L 

u 4uL u 2L u 

1 

t 

( L 

xxt 

t 

x 

 

x 

u 4uL u 2L u 

t 

x 

L udx L u), 

 

x 

t 

x 

L udx L u), 

t 

x 

(27) 

(28) 

is found. Here the main point is that the solution of the decomposition 

method is in the form of 

u ( x, 

t) 

un 

( x, 

t) 

, (29) 

n0 

Substituting from Eq. 29 in 28, we find 

 

 

n0 

 

 

 

 

L ( , ) 4 ( , ) ( , ) 

1 

0 

0 

0 

( , ) ( ,0) 

 

 

 

xxt 

un 

x t 

un 

x t Lt 

 

un 

x t 

n 

n 

n 

 

u 

n 

x t u x Lt 

 

, (30) 

 

x 

 

 

 

2 ( , ) 

( , ) 

( , ) 

Lx 

 

un 

x t 

Lt 

 

un 

x t dx 

Lx 

 

un 

x t 

n0 

n0 

n0 

 

is found. 

According to Eq.19 approximate solution can be obtained as follows: 

 

2 1 c 1 

 

( c 1)sech 

x 

2 c 

u0 

( x, 

t) 

 

 

, 

2c 

1 c 1 

c 1 

( c 1)sinh 

 

x 

2 

t 

1( 

, ) 

c c 

x t 

, 

 

3 1 c 1 

 

2c 

cosh 

x 

2 

c 

(31) 

u (32) 

t 

 

(33) 

u2( x, 

t) 

( Lxxtu1 

4u1Lt 

u1 

2Lxu1 

Lt 

u1dx 

Lxu1 

) dt, 

0 

Thus the approximate solution for first model of shallow water wave 

equation is obtained as 

u x, 

t) 

u ( x, 

t) 

u ( x, 

t) 

u ( x, 

) , (34) 

( 

0 1 

2 

t 

The terms u0 ( x, 

t), 

u1( 

x, 

t), 

u2 

( x, 

t) 

in Eq.34, obtained from 

Eqs.31, 32, 33. In Fig.1 the first model of shallow water wave equation 

with the first initial condition (31) of Eq. (2) when c=2 has been shown. 

ADM IMPLEMENT FOR SECOND MODEL OF SHALLOW 

WATER WAVE EQUATION 

Now we consider the application of ADM to second model of shallow 

water wave equation. If Eq. (3) is dealt with this method, it is formed as 

x 




Mehdi Safari 

L u L u 3uL u 3L u L udx L u, 

(35) 

t 

where 

xxt 

t 

3 

 

 

L t 

, L x 

, L xxt 

, 

2 

t x x 

t 

x 

x 

t 

x 

(36) 

The terms u0 ( x, 

t), 

u1( 

x, 

t), 

u2 

( x, 

t) 

in Eq.44, obtained from 

Eqs.41, 42, 43. If we assume c=2 then by drawing 3-D figures of ADM 

solutions. In Fig.2 the second model of shallow water wave equation 

with the first initial condition (31) of Eq. (2) when c=2 has been shown. 

Fig.1. For the first model of shallow water wave equation with the first 

initial condition (31) of Eq. (2), ADM result for u ( x, 

t) 

, when c=2. 

If the invertible operator 

L L u L 

1 

t 

t 

1 

t 

( L 

xxt 

L 

1 

t 

t 

dt 

u 3uL u 3L u 

t 

0 

x 

is applied to Eq. 45, then 

 

x 

L udx L u), 

t 

x 

(37) 

is obtained. By this 

u( 

x, 

t) 

u( 

x,0) 

L 

1 

t 

( L 

xxt 

u 3uL u 3L u 

t 

x 

 

x 

L udx L u), 

t 

x 

(38) 

is found. Here the main point is that the solution of the decomposition 

method is in the form of 

u ( x, 

t) 

un 

( x, 

t) 

, (39) 

n0 

Substituting from Eq. 49 in 48, we find 

Fig.2. For the second model of shallow water wave equation with the 

first initial condition (31) of Eq. (3), ADM result for u ( x, 

t) 

, when 

c=2. 

 

 

n0 

 

 

 

 

L ( , ) 3 ( , ) ( , ) 

1 

0 

0 

0 

( , ) ( ,0) 

 

 

 

xxtun 

x t un 

x t Lt 

un 

x t 

n 

n 

n 

 

u 

n 

x t u x Lt 

 

, (40) 

 

x 

 

 

 

3 ( , ) ( , ) 

( , ) 

Lx 

un 

x t 

Lt 

un 

x t dx 

Lx 

un 

x t 

n0 

n0 

n0 

 

is found. 

According to Eq.19 approximate solution can be obtained as follows: 

 

2 1 c 1 

 

( c 1)sech 

x 

2 c 

u0 

( x, 

t) 

 

 

, 

2c 

1 c 1 

c 1 

( c 1)sinh 

 

x 

2 

t 

1( 

, ) 

c c 

x t 

, 

 

3 1 c 1 

 

2ccosh 

 

x 

2 

c 

(41) 

u (42) 

t 

 

(43) 

u2( x, 

t) 

( Lxxtu1 

3u1L tu1 

3Lxu1 

Lt 

u1dx 

Lxu1 

) dt, 

0 

Thus the approximate solution for second model of shallow water wave 

equation is obtained as 

u( x, 

t) 

u0 ( x, 

t) 

u1( 

x, 

t) 

u2 

( x, 

t) 

, (44) 

x 

CONCLUSION 

In this paper, Adomian’s decomposition method has been successfully 

applied to find the solution of two model equations for shallow water 

waves. The obtained results were showed graphically it is proved that 

Adomian's decomposition method is a powerful method for solving 

these equations. In our work; we used the Maple Package to calculate 

the functions obtained from the Adomian’s decomposition method. 




Mehdi Safari 

REFERENCES 

K. Abbaoui, Y. Cherruault, "The decomposition method applied to the 

Cauchy problem", Kybernetes , Vol.28, 1999, 103. 

M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur," The inverse 

scattering transform-Fourier analysis for nonlinear problems ", Studies 

in Applied Mathematics, Vol.53, 1974, pp. 249-315. 

G. Adomian, "An analytical solution of the stochastic Navier-Stokes 

system ", Foundations of Physics, Vol.21, No.7, 1991, pp.831-843. 

G. Adomian, "Solution of physical problems by decomposition", 

Computers and Mathematics with Applications, Vol.27, No.9/10, 1994, 

pp.145-154. 

G. Adomian, "Solutions of nonlinear PDE", Applied 

Mathematics Letters, Vol.11, No.3, 1998, pp.121-123. 

G. Adomian, R. Rach, " Linear and nonlinear Schrödinger equations ", 

Foundations of Physics, Vol.21, 1991, pp.983-991. 

P.A. Clarkson and E.L. Mansfield, "on a shallow water wave equation", 

Nonlinearity, Vol.7, 1994, pp. 975-1000. 

D.D. Ganji, M. Safari, R. Ghayor, "Application of He's variational 

iteration method and Adomian's decomposition method to Sawada– 

Kotera–Ito seventh-order equation", Numerical Methods for Partial 

Differential Equations, Vol. 27, No,4,2011, pp: 887-897. 

D.D. Ganji, E. M. M. Sadeghi, M. Safari, "Application of He's 

variational iteration method and adomian's decomposition method 

method to Prochhammer Chree equation", International Journal of 

Modern Physics B, Vol. 23, No. 3, 2009, pp.435-446. 

R. Hirota and J.Satsuma," N-Soliton solutions of model equations for 

shallow water waves", Journal of the Physical Society of Japan, Vol.40, 

No.2, 1976, pp.611-612. 

D. Kaya, A. Yokus, "A numerical comparison of partial solutions in 

thedecomposition method for linear and nonlinear partial differential 

equations", Mathematics and Computers in Simulation, Vol.60, No.6, 

2002, pp.507-512. 

M. Safari, D.D. Ganji, M. Moslemi , "Application of He's variational 

iteration method and Adomian's decomposition method to the fractional 

KdV-Burgers-Kuramoto equation", Computers and Mathematics with 

Applications, Vol.58, 2009, pp. 2091-2097. 

A.M.Wazwaz, "Partial Differential Equations: Methods and 

Applications", Balkema, Rottesda 2002. 

A.M.Wazwaz, "A First Course in Integral Equations", World Scientific, 

Singapore, 1997. 

A.M.Wazwaz, "A new algorithm for calculating Adomian polynomials 

for nonlinear operators ", Applied Mathematics and Computation, 

Vol.111, No.1, 2000, pp.33-51. 

A.M.Wazwaz, "A reliable modification of Adomian decomposition 

method", Applied Mathematics and Computation, Vol.102, No.1, 

1999, pp.77-86. 



Dr. Jasem M.S. Alrajhi, Dr. Hilal A. Abdelwali, Dr. Mohsen S. Al-Ardhi, Eng. Rafik El Shiaty 

On Bicriteria Large Scale Transshipment Problems 

Dr. Jasem M.S. Al-Rajhi* ajasem@gmail.com 

Dr. Hilal A. Abdelwali* haabdelwali@hotmail.com 

Dr. Mohsen S. Al-Ardhi* malardhi@hotmail.com 

Eng. Rafik El Shiaty** rmshiaty@engineer.com 

* Assistant Professor, Automotive and Marine Department, College of Technological Studies, PAAET, Kuwait. 

**Lecturer, Power and Refrigeration Technology Department, College of Technological Studies, PAAET, Kuwait. 

ABSTRACT 

In this paper, several bicriteria multistage transportation problems with transshipment (BMTSP) are formulated. An algorithm for solving a certain 

class of (BMTSP) is presented. The mathematical formulation of this class does not affect the special structure of the transshipment problem for each 

of the individual stages. The presented algorithm is mainly based on a fruitful application of the methods of solving bicriteria single stage 

transportation problems, available decomposition techniques for solving large scale linear programming problems, and the methods of treating the 

transshipment problems. An illustrative example is included. 

Keywords: Large Scale Transportation Problem, Transshipment Problem. Multiobjective Decision Making, Decomposition Technique of Linear 

Programming. 

INTRODUCTION 

The classical transportation problems allow only shipments that go 

directly from a supply point to a demand point, i.e. shipments do not 

take place between origins or between destinations, nor from 

destinations to origins. In many situations, shipments are allowed 

between supply points or between demand points. Sometimes there 

many also be points (called transshipment points) through which goods 

can be transshipped on their journey from a supply point to a demand 

point. Shipping problems with any or all of these characteristics are 

transshipment problems. A transshipment problem was first introduced 

by Orden (1965) [1]. He introduced an extension of the original 

transportation problem to include the possibility of transshipment. The 

problem of determining simultaneously the flows of primary products 

through processors to the market of final products has been formulated 

alternatively as a transshipment model by King and Logan [2] and as a 

reduced matrix model by Rhody (1963) [3]. An extension of this 

problem to a multi regional, multi product, and multi plant problem 

formulated in the form of general linear programming model has been 

proposed by Judge et al (1965) [4]. Afterwards, various alternative 

formulations of the transshipment problem within the framework of the 

transportation model that permits solution of problems of the type 

discussed by King and Logan without the need for subtraction of 

artificial variables were discussed by Hurt and Tramel (1965) [5]. Grag 

and Prakash (1985) [6] studied time m inimizing transshipment 

problem. Later dynamic transshipment problem was studied by Herer 

and Tzur (2001) [7]. Afterwards multi location transshipment problem 

with capacitated production and lost sales was studied by Ozdemir 

(2006) [8]. Osman M.S.A. et al (1984) [9] introduced an algorithm for 

solving bicriteria multistage transportation problems. Recently, 

Khurana et al (2011) [10] studied a transshipment problem with mixed 

constraints. Also. In (2012) Khurana et al [11] they introduced an 

algorithm for solving time minimizing capacitated transshipment 

problem. Yousria Abo-elnaga et al (2012) [12] introduced a trust region 

globalization strategy to solve multi-objective transportation, 

assignment, and transshipment problems. In this paper formulation of 

different structures of bicriteria large scale transshipment problems, and 

an algorithm for solving a class of them which can be solved using the 

decomposition technique of linear programming utilizing the special 

nature of transshipment problems are presented. The presented 

algorithm determines the points of the non-dominated set in the 

objective space. The method consists of solving the same multistage 

transshipment problem repeatedly but with different objectives and 

each iteration gives either a new non dominated extreme point or 

changes the direction of search in the objective space. An illustrative 

example is presented in this paper. 

Formulation of Bicriteria Multistage Transshipment Problems 

The formulation of different bicriteria multistage transportation 

problems with transshipment presented in this paper covers several real 

situations. 

Bicriteria Multistage Transportation Problem with Transshipment 

of the First kind (BMTSP 1) 

This case represents multistage transshipment problems without any 

restrictions on intermediate stages. 

In order to obtain the mathematical formulation of the problems 

representing this case let us assume that the availabilities are (a j ), j= 1, 

2, 3, …., n; n is the number of (sources + destinations); the 

requirements are (b j ), j= 1, 2, 3, ….., n; the minimum transportation 

costs and deteriorations from i to j are (c ij ),(d ij) i= 1, 2, 3, …., n; j= 1, 2, 

3, …., n; (x ij ) denotes the quatity shipped from i to j; and (x jj ) is the neat 

amount transshipped through point j, x ij ≥0. Then the problem takes the 

form: 

n n 

Min. 

Z 

1 

 

 

i 1 j 1 

c ij 

x ij 




Z 

 

n 

n 

 

d ij 

x ij 

2 

i 1 j 1 

With c ij = 0 for the quantity shipped from the source (S i ) to itself and 

from destination (D j ) to itself. 

Subject to: 

n 

 

i1 

i 

j 

n 

 

i1 

i 

j 

x 

x 

ji 

ij 

x 

x 

x ij ≥ 0 for all i, j. 

ij 

ji 

a 

b 

j 

j 

, j 1,2,..., 

n. 

, j 1,2,..., 

n. 


of the Second Kind (BMTSP 2): 

This case represents bicriteria multistage transshipment problems in 

which the transportation at any stage is independent of the 

transportation at the other stages. 

In order to obtain the mathematical formulation of the problem 

representing this case let us assume that for k th stage, k= 1, 2, 3, …., N; 

k 

the availabilities are: ( a 

jk 

), jk 

1,2,3 ,... nk 

, n k is the number of 

(sources + destinations) at the k th stage; the requirements are: 

k 

( b 

jk 

), jk 

1,2,3,... 

nk 

; the transportation costs and deteriorations 

are c k i j , d k 

i j i = 1, 2, 3, ., n ; j = 1, 2, 3, ., n ; 

k k k k 

k k 

k 

quantity shipped from i k 

k 

to j k ; and 

k 

transshipped through point j k , x 

j k j 

0 . 

k 

Then the problem takes the form: 


Z 

Z 

k 

2 

k 

1 

 

 

n 

n 

n 

 

k k 

ik 

1 jk 

1 

n 

k k 

 

ik 

1 jk 

1 

d 

c 

k 

ik 

jk 

k 

ik 

jk 

x 

x 

k 

ik 

jk 

k 

ik 

jk 

x 

k 

j k j k 

x 

k 

i j denotes the 

k k 

is the net amount 

k 

With ci 

j 

0 for the quantity shipped from the source (S i ) to itself 

k k 

and from the destination (D j ) to itself. 

Subject to: 

k 

 

ik 

1 

i j 

k 

n 

k 

k 

 

ik 

1 

i j 

k 

n 

k 

x 

x 

k 

j i 

k k 

k 

i j 

k k 

x 

x 

k 

j j 

k k 

k 

j j 

k k 

a 

b 

k 

j 

k 

k 

j 

k 

, j 

, j 

k 

k 

1,2,..., 

n. 

1,2,..., 

n. 

x ij ≥ 0 for all i k , j k. 

and the minimum transportation cost is given by: 

MinZ 

n 

 

k1 

MinZ 

k 


of the Third Kind (BMTSP 3): 

This case represents bicriteria multistage transshipment problems with 

some additional transportation restrictions on the intermediate stages 

which does not affect the transshipment problem formulation at each 

stage. 

The mathematical formulation of the problem representing this case is 

given as: 


Z 

... 

n 

N 

1 

 

n 

N 

 

iN 

1 jN 

1 

Z 

2 

 

n1 

n1 

 

i1 

1 j1 

1 

c i 

x 

N 

N jN 

n1 

n1 

 

i1 

1 j1 

1 

... 

n 

N 

n 

k k 

 

1 1 

k k 

ci 

... 

... 

1 j 

x 

1 i1 

j 

c 

1 

ik 

j 

x 

k ik 

jk 

N 

iN 

jN 

n 

ik 

1 jk 

1 

n 

k k 

 

1 1 

k k 

di 

... 

... 

1 j 

x 

1 i1 

j 

d 

1 

ik 

j 

x 

k ik 

jk 

n 

N 

 

iN 

1 jN 

1 

d i 

x 

N 

N jN 

N 

iN 

jN 

n 

ik 

1 jk 

1 

k 

with ci 

k j and d k 

k ik 

j = 0 for the quantity shipped from the source ( k 

S 

k 

i ) 

k 

k 

to itself and from the destination ( D 

j ) to itself: k = 1, 2, …, N subject 

k 

to: 

n1 

1 1 1 

x 

j 

, 

1 

1,2,..., 

1i 

x a j n 

1 j1 

j 

 

1 j 

 

1 

1 

i1 

1 

i j 

1 

n 

1 

1 

 

i1 

j 

i1 

1 

. 

. 

. 

n 

i 

i 

1 

k 

 

k 

k 

j 

1 

n 

k 

k 

 

ik 

j 

ik 

1 

. 

. 

k 

x 

1 1 1 

i 

, 

1 

1,2,..., 

1 j 

x b j n 

1 j1 

j 

 

1 j 

 

1 

1 

x 

x 

k k k 

j j 

x 

j j 

a 

j 

, j 

k k k k k k 

1,2,..., 

k k k 

i j 

x 

j j 

bj 

, j 

k k k k k k 

1,2,..., 

n 

n 

k 

k 




Z 

. 

i 

i 

n 

N 

 

N 

N 

i 

i 

j 

1 

n 

j 

1 

N 

N 

 

N 

N 

F 

x 

N 

x 

x 

N N N 

j i 

x 

j j 

a 

j 

, j 

N N N N 

N N 

1,2,..., 

N N N 

i j 

x 

j j 

bj 

, j 

N N N N N N 

1,2,..., 

k1 

k k1 

( xi 

, , ) 0, 

1 j 

x 

1 

i j 

x 

k k k k ik 

1 

jk 

1 

k 

N 

0,.., x 

k 

0,.. x 0 

rk 

1 

i 

 

1 j1 

i jk 

iN 

jN 

For all i1,..., iK 

,..., iN 

; j1,..., 

jK 

,..., jN 

; 

where: 

F 

k 

r 

, k 1,2,..., 

N are linear functions representing the 

additional transportation restrictions and r k is the number of this linear 

functions at the k th stage. 


of the Fourth Kind (BMTSP 4) 

This case represents bicriteria multistage transshipment problems in 

which the difference between the input and output transportation 

commodity is known at the sources (destinations) of each intermediate 

stage. The assumed transportation restrictions in this case affect the 

transshipment formulation in each individual stage. 

The mathematical formulation of the problem representing this case is 

given as: 

2 


Z 

... 

 

... 

1 

n 

N 

 

n 

N 

 

iN 

1 jN 

1 

n1 

n1 

 

i1 

1 j1 

1 

n 

N 

N 

 

iN 

1 jN 

1 

n1 

n1 

 

i1 

1 j1 

1 

c i 

x 

N 

N jN 

n 

k k 

 

1 1 

k k 

ci 

... 

... 

1 j 

x 

1 i1 

j 

c 

1 

ik 

j 

x 

k ik 

jk 

N 

iN 

jN 

n 

k k 

 

n 

n 

n 

ik 

1 jk 

1 

1 1 

k k 

di 

... 

... 

1 j 

x 

1 i1 

j 

d 

1 

ik 

j 

x 

k ik 

jk 

n 

d i 

x 

N 

N jN 

N 

iN 

jN 

n 

ik 

1 jk 

1 

k 

with ci 

k j and d k 

k ik 

j = 0 for the quantity shipped from the source ( k 

S 

k 

i ) 

k 

k 

to itself and from the destination ( D 

j ) to itself: k = 1, 2, …, N subject 

k 

to: 

n1 

1 1 1 

x 

j 

, 

1 

1,2,..., 

1i 

x a j n 

1 j1 

j 

 

1 j 

 

1 

1 

i1 

j1 

i 1 

1 

n1 

 

i1 

j1 

i1 

1 

. 

. 

n 

1 1 

( 2 

2 2 1 

i 

) , 

1 

1,2,..., 

1; 

2 

1,2,... 

1 j 

x 

1 j1 

j 

 

1 x 

j 

x b j n j n 

2i 

 

2 j2 

j 

 

2 j 

 

1 

2 

i2 

j2 

i2 

1 

x 

N 

N 

. 

nk 

1 

nk 

k1 

k1 

k k k1 

xi 

j 

x 

j j 

( x 

j i 

x 

j j 

) bj 

, jk 

1,2,..., nk 

; jk 

1,2,... 

n 

k k 

k k 

k k k k 

k 1 

 

1 

 

1 1 

1 

1 

 

1 

 

 

k 

ik 

1 

jk 

1 

ik 

jk 

ik 

1 

ik 

1 

i 

i 

j 

n 

N 1 

 

N 1 

N 1 

i 

i 

j 

1 

N 1 

n 

N 

 

N 

N 

x 

j 

1 

k 

i j 

k 

k 

x 

N 1 

N 

N 1 

i j 

N 1 

N 1 

x 

1,2,..., 

n 

x 

N 1 

j j 

N 1 

N 1 

N 1 

; j 

N 

( 

i 

i 

n 

N 

 

N 

N 

j 

1 

N 

x 

1,2,... 

n 

N 

j i 

N N 

N 

x 

N N N 

i j 

x 

j j 

bj 

, j 

N N N N N N 

1,2,..., 

0 

for all i k , j k ; k=1, 2, …, N 

n 

N 

j j 

N N 

N 

) b 

N 1 

j 

N 1 

(BMTSP 1) is solved as a bicriteria single stage transshipment problem. 

(BMTSP 2) can be solved as N single stage biceriteria transshipment 

problems and the minimum value of the total transport costs and 

deteriorations are obtained as the sum of the minimum transportation 

costs and deteriorations for each individual stage. 

(BMTST3) can be solved using the decomposition technique utilizing 

the special nature of transshipment problems. The next section will be 

devoted to the solution of this type of problems. 

(BMTSP4) is solved using any method for solving bicriteria linear 

programming problems. 

An Algorithm for Solving BMTSP 3 

The decomposition technique of linear programming can be used to 

solve the bicriteria multistage transshipment problems especially that of 

the (BMTSP 3) type. 

This type of bicriteria multistage transshipment problems decomposed 

into [2, 3, 5, 8]: 

a) Sub problems corresponding to every stage. 

b) A master program which ties together the sub problems. 

Let: 

Dk be the matrix consisting of the coefficients of k the 

subproblem constraints. 

Ak be the matrix consisting of the coefficients of k th stage tiein 

constraints. 

b be the vector of constant coefficients in the tie-in 

constraints. 

bk be the vector consisting of the availabilities and 

requirements of kth sub-problem . 

Ro be the matrix consisting of the first mo columns of B-1, mo 

denotes the number of elements of b, B be the current basis 

matrix. 

ck be the vector of first objective coefficients of kth subproblem 

. 

dk be the vector of second objective coefficients of kth subproblem 

. 

cB be the corresponding vector of basic variables coefficients. 

N be the number of subproblems. 

, 




In the following we will present an algorithm for determining all 

nondominated extreme points of the (BMTSP3) model from which the 

solution of the (BMTSP1) and the (BMTSP2) models can be deduced 

as special cases from it. 

Let: for independent constraints: 

D k , k= 1,2,…,N be the technological matrix of the k th stage activity, D k 

is (m k + n k ) * (m k + n k ) matrix, N is the number of stages, m k is the 

number of sources at k th stage, n k is the number of destinations. 

b k be the column vector consisting of the availabilities and 

requirements of the k th subproblem, b k is (m k + n k ) * 1 column vector. 

It follows that each set of independent constraints can be written as: 

D k x k = b k , k = 1,2,…,N 

x k represent the vector of the corresponding variables, x k is (m k + n k ) *1 

column vector. 

Let: For the common constraints: 

A k be the technogical matrix of k th stage activity, A k is m 0 * (m k * n k ) 

matrix, m 0 be the number of common constraints. 

b 0 be its corresponding common resources vector, b 0 is (m 0 * 1) column 

vector. 

This gives: A 1 x 1 + A 2 x 2 + …….+ A k x k + ……. +A N x N = b 0 

Let: for the objective functions: 

c K represent the vector of the first criterion coefficients for the k th stage 

activity, c k is 1*(m k *n k ) row vector. 

d k represent the vector of the second criterion coefficients for the k th 

stage activity, d k is 1*(m k *n k ) row vector. 

Let: For the master program: 

B be the basic matrix associated with the current basic solution, B is 

(m o *N) * (m o +N) matrix. 

C B be the row vector of the corresponding coefficients in the objective 

function, C B is 1*(m o +N) row vector. 

R o is the matrix of size (m o + N)*m o consisting of the first m o columns 

of B -1 , and 

v j is the (m o + j) th column of the same matrix B -1 

The algorithm presented here is divided into two phases. 

Phase 1: Determine the nondominated extreme points in the objective 

space. And the algorithm is validated by the following theorem [1]. 

Theorem: 

A point z (q) q 

q 

= z1 , z2 

is a nondominated extreme point is the 

objective space if and only if z(q) is recorded by the algorithm. 

Phase II: Is the decomposition algorithm which can be found in [7]. 

Since the special structure of the (BMTSP3) model may allow the 

determination of the optimal solution by, first decomposing the 

problem into small subproblems and then solving those subproblems 

almost independently, then the decomposition algorithm for solving 

large scale linear programming problems utilizing the special nature of 

transshipment problem can be used to solve it. 

Phase I: 

Step 1: Go to phase II, find 

z 

(1 ) Min z / x M 

1 

 

And find 

. 

1 

(1) 

(1) 

z 

2 

Min . z 

2 

/ z 

1 

z 

1 

and x M . 

Step 2: 

(1) (1) 

Record ( z 

1 , z 

2 ) and set q = 1. 

Similarly, go to phase II, find 

z 

( 2 ) 

2 

 

And find 

 


2 

/ x 

( 2 ) 

( 2 ) 

z 

1 


1 

/ z 

2 

z 

2 

and x M . 

( 2 ) ( 2 ) (1) (1) 

( z 

1 

, z 

2 

) ( z 

1 

, z 

2 

), stop 

M 

If . 

(2) (2) 

Otherwise record ( z 

1 , z 

2 ) and set q = q+1 

Defines sets L = {(1,2)} and E = , and go to step 2. 

Choose an element (r,s) L and set 

( r , s ) ( s ) ( r ) 

a z z and 

a 

1 

( r , s ) 

2 

 

z 

2 

( s ) 

1 

 

z 

2 

( r ) 

1 

k 

Go to phase II to obtain the optimal solution ( x , k=1,2,..,N) to the 

multistage transshipment problem. 

Minimize 

x 

k 

N 

 

k 1 

 

ik 

, jk 

and 

( r, 

s) 

k 

( r, 

s) 

k 

(e 

1 

cik 

j 

a d 

k 2 ik 

j 

) 

k 

Subject to 

k 

M , x o , k 1,2 ,.., N 

 

x 

k 

ik 

jk 

If there are alternative optima, choose an optimal solution 

k=1,2,.,N, for which 

N 

 

k 1 

 

ik 

, jk 

Let z 

1 

= 

z 

2 

= 

N 

 

k1 

( c 

N 

 

k1 

k 

ik 

jk 

 

i , j 

k 

x 

 

ik 

, jk 

k 

k 

ik 

jk 

d 

c 

k 

ik 

jk 

k 

i j 

k k 

min.) 

x 

x 

k 

ik 

jk 

k 

i j 

k k 

; and 

( r ) ( r ) 

If ( z 

1 

, 

2 

( z 

1 

, z 

2 

) 

Set E = E {(r,s)} and go to step 3. 

( q) 

( q) 

Otherwise record ( z 

1 

, z 

2 ) such that 

z 

( s ) ( s ) 

z ) is equal to or ( z , z ) 

( q ) 

( q ) 

1 

z1 

, z 

2 

z 2 and set q q 

Step 3: 

L = L {(r,q)}, (q,s)} and go to step 3. 

Set L = L - {(r-s)}. If L = , stop. 

Otherwise go to step 2. 

1 

1, 

2 

k 

x , 

Phase II: 

Step 1: Reduce the original problem to the modified form in terms of 

the new variables k 

Step 2: Find an initial basic feasible solution to the modified problem. 

Step 3: Solve the subproblems 

k k 

k 

k k 

w ( c OR d c 

B 

R 

o 

A ) x 

Subject to 

k k k 

D x b , 

x k 

o , k 1,2,..., N . 




Note: c k will be used with first criteria, and d k will be used with the 

second criteria. 

Obtaining 

xˆ 

k 

l 

and optimal objective values 

transportation technique, Go to step 4. 

Step 4: For the current iteration, find 

* k 

k 

k 

w c 

B 

v , k 

k 

Then determine Min ( ) 

k 

1,2,..., N , 

k 

w * 

, by using the 

If o , the current solution is optimal and the process is 

terminated, the optimal solution to multistage transportation problem is: 

x 

k 

 

L 

 

 

K 

L 

K 

xl , 

k 

1,2 ,..., 

L 1 

Otherwise, go to step 5. 

k 

Step 5: Introduce the variable 

L corresponding to into the basic 

solution. Determine the leaving variable using the feasibility condition 

and compute the next B -1 using the revised simplex method technique, 

go to step 3. 

Illustrative Example 

The suggested algorithm for solving problem of the type BMTSP 3 will 

be illustrated in the following example: 

Consider the following bicriteria two stage transshipment problem. For 

each stage the availabilities, requirements, costs and deteriorations for 

each stage are given as: 

1 

a 

1 = 6, 

2 

b 

1 = 6, 

1 

a 

2 = 4, 

a = 2, 

1 

3 

2 2 

b 

2 = 2, b 

3 

= 4 

1 

b 

1 = 

N 

2 

a 

1 = 9, 

1 

b 

2 = 

Table 1. Transportation cost at stages (1) and (2). 

D 1 1 D 1 2 S 1 1 S 1 2 S 1 3 

S 1 1 5 4 0 2 1 

S 1 2 10 8 1 0 4 

S 1 3 9 9 3 2 0 

D 1 1 0 1 5 9 9 

D 1 2 3 0 4 6 7 

D 2 1 D 2 2 D 2 3 S 2 1 S 2 2 

S 2 1 4 3 3 0 3 

S 2 2 8 4 7 2 0 

D 2 1 0 2 4 8 7 

D 2 2 4 0 3 3 5 

D 2 3 3 4 0 4 9 

Table 2. Deterioration cost at stages (1) and (2). 

D 1 1 D 1 2 S 1 1 S 1 2 S 1 3 

S 1 1 3 6 0 1 4 

S 1 2 7 9 3 0 6 

S 1 3 12 11 4 6 0 

D 1 1 0 3 7 11 12 

D 1 2 5 0 7 8 8 

2 

a 

2 = 3, 

D 2 1 D 2 2 D 2 3 S 2 1 S 2 2 

S 2 1 6 5 5 0 6 

S 2 2 11 6 9 5 0 

D 2 1 0 4 6 11 9 

D 2 2 6 0 5 4 7 

D 2 3 5 7 0 6 11 

One requirement is added to the above problem: 

It is required that the quantity shipped from the first source to the first 

destination in the first stage is equal to the quantity shipped from the 

first source to the first destination in the second stage. 

The mathematical model is given as follows: 

Minimize z 1 = 5x 1 11 + 4x 1 12 + 0x 1 13 + 2x 1 14 + x 1 15 

+ 10x 1 21 + 8x 1 22 + x 1 23 + 0x 1 24 + 4x 1 25 

+ 9x 1 31 + 9x 1 32 + 3x 1 33 + 2x 1 34 + 0x 1 35 

+ 0x 1 41 + x 1 42 + 5x 1 43 + 9x 1 44 + 9x 1 45 

+ 3x 1 51 + 0x 1 52 + 4x 1 53 + 6x 1 54 + 7x 1 55 

+ 4x 2 11 + 3x 2 12 + 2x 2 13 + 0x 2 14 + 3x 2 15 

+ 8x 2 21 + 4x 2 22 + 7x 2 23 + 2x 2 24 + 0x 2 25 

+ 0x 2 31 + 2x 2 32 + 4x 2 33 + 8x 2 34 + 7x 2 35 

+ 4x 2 41 + 0x 2 42 + 3x 2 43 + 3x 2 44 + 5x 2 45 

+ 3x 2 51 + 4x 2 52 + 0x 2 53 + 4x 2 54 + 9x 2 55 

Subject to: 

Z 2 = 3x 1 11 + 6x 1 12 + 0x 1 13 + 1x 1 14 + 4x 1 15 

+ 7x 1 21 + 9x 1 22 + 3x 1 23 + 0x 1 24 + 6x 1 25 

+ 12x 1 31 + 11x 1 32 + 4x 1 33 + 6x 1 34 + 0x 1 35 

+ 0x 1 41 + 3x 1 42 + 7x 1 43 + 11x 1 44 + 12x 1 45 

+ 5x 1 51 + 0x 1 52 + 7x 1 53 + 8x 1 54 + 8x 1 55 

+ 6x 2 11 + 5x 2 12 + 5x 2 13 + 0x 2 14 + 6x 2 15 

+ 11x 2 21 + 6x 2 22 + 9x 2 23 + 5x 2 24 + 0x 2 25 

+ 0x 2 31 + 4x 2 32 + 6x 2 33 + 11x 2 34 + 9x 2 35 

+ 6x 2 41 + 0x 2 42 + 5x 2 43 + 4x 2 44 + 7x 2 45 

+ 5x 2 51 + 7x 2 52 + 0x 2 53 + 6x 2 54 + 11x 2 55 

x 1 11 = x 2 11 

x 1 11 + x 1 12 + x 1 13 + x 1 14 + x 1 15 = 18 

x 1 21 + x 1 22 + x 1 23 + x 1 24 + x 1 25 = 16 

x 1 31 + x 1 32 + x 1 33 + x 1 34 + x 1 35 = 14 

x 1 41 + x 1 42 + x 1 43 + x 1 44 + x 1 45 = 12 

x 1 51 + x 1 52 + x 1 53 + x 1 54 + x 1 55 = 12 

x 1 11 + x 1 21 + x 1 31 + x 1 41 + x 1 51 = 21 

x 1 12 + x 1 22 + x 1 32 + x 1 42 + x 1 52 = 15 

x 1 13 + x 1 23 + x 1 33 + x 1 43 + x 1 53 = 12 

x 1 14 + x 1 24 + x 1 34 + x 1 44 + x 1 54 = 12 

x 1 15 + x 1 25 + x 1 35 + x 1 45 + x 1 55 = 12 

x 2 11 + x 2 12 + x 2 13 + x 2 14 + x 2 15 = 21 

x 2 21 + x 2 22 + x 2 23 + x 2 24 + x 2 25 = 15 

x 2 31 + x 2 32 + x 2 33 + x 2 34 + x 2 35 = 12 

x 2 41 + x 2 42 + x 2 43 + x 2 44 + x 2 45 = 12 

x 2 51 + x 2 52 + x 2 53 + x 2 54 + x 2 55 = 12 

x 2 11 + x 2 21 + x 2 31 + x 2 41 + x 2 51 = 18 

x 2 12 + x 2 22 + x 2 32 + x 2 42 + x 2 52 = 14 

x 2 13 + x 2 23 + x 2 33 + x 2 43 + x 2 53 = 16 

x 2 14 + x 2 24 + x 2 34 + x 2 44 + x 2 54 = 12 

x 2 15 + x 2 25 + x 2 35 + x 2 45 + x 2 55 = 12 




and all x 1 0, 

2 

i 

0 

1 j 

x 

1 i2 

j for all i 1 = 1, 2, ……, 5; 

2 

j 1 = 1, 2, …., 5 ; i 2 = 1, 2, …….., 5 ; j 2 = 1, 2, ….., 5. 

The problem can be decomposed into two sub problems, k = 1, 2. 

9 Z 9 = 

(113,156) 

CONCLUSION 

X 1 11=6, X 1 12=4, X 1 13=8, X 1 23=4, X 1 24=12, X 1 31=2, 

X 1 35=12, X 1 41=12, X 1 51=1, X 1 52=11, X 2 11=6, 

X 2 13=4, X 2 14=11, X 2 22=2, X 2 24=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

The following Table (3) gives phase 1 iterations (solution of bicriteria in the 

objective space). 

Table 3. Set of non dominated extreme points. 

Iteration L E Recorded 

Point 

1 

2 

3 

4 

5 

6 

7 

8 

9 

{(1,2)} 

{(1,2)} 

{(1,3),(3,2)} 

{(3,2), (1,4), (4,3)} 

{(1,4), (4,3), (3,5), 

(5,2)} 

{(1,4), (4,3), (3,5)} 

{(1,4), (4,3)} 

{(1,4)} 

 

 

 

 

 

 

{(5,2)} 

{(5,2), (3,5)} 

{(5,2), (3,5), (4,3)} 

{(5,2), (3,5), (4,3), 

(1,4)} 

Table 4. Non zero value of X ij for each non dominated point 

Iteration Non 

Non zero value of X ij 

dominated 

(Z 1 , Z 2 ) 

1 Z 1 = 

(113,156) 

Z 1 = (113,156) 

Z 2 =(127,140) 

Z 3 = (121,141) 

Z 4 = (115,149) 

Z 5 = (124,140) 

Z 6 = (124,140) 

Z 7 = (124,140) 

Z 8 = (115,149) 

Z 9 = (113,156) 

X 1 11=6, X 1 12=4, X 1 13=8, X 1 23=4, X 1 24=12, X 1 31=2, 

X 1 35=12, X 1 41=12, X 1 51=1, X 1 52=11, X 2 11=6, 

X 2 13=4, X 2 14=11, X 2 22=2, X 2 24=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

2 Z 2 =(127,140) X 1 11=6, X 1 12=2, X 1 13=10, X 1 21=3, X 1 22=1, X 1 24=12, 

X 1 33=2, X 1 35=12, X 1 41=12, X 1 52=12, X 2 11=6, 

X 2 13=3, X 2 14=12, X 2 22=2, X 2 23=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

3 Z 3 = 

(121,141) 

4 Z 4 = 

(115,149) 

5 Z 5 = 

(124,140) 

6 Z 6 = 

(124,140) 

7 Z 7 = 

(124,140) 

8 Z 8 = 

(115,149) 

X 1 11=6, X 1 12=3, X 1 13=9, X 1 21=3, X 1 23=1, X 1 24=12, 

X 1 33=2, X 1 35=12, X 1 41=12, X 1 52=12, X 2 11=6, 

X 2 13=4, X 2 14=11, X 2 22=2, X 2 24=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

X 1 11=6, X 1 12=3, X 1 13=9, X 1 21=1, X 1 23=3, X 1 24=12, 

X 1 31=2, X 1 35=12, X 1 41=12, X 1 52=12, X 2 11=6, 

X 2 13=4, X 2 14=11, X 2 22=2, X 2 24=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

X 1 11=6, X 1 12=3, X 1 13=9, X 1 21=3, X 1 23=1, X 1 24=12, 

X 1 33=2, X 1 35=12, X 1 41=12, X 1 52=12, X 2 11=6, 

X 2 13=3, X 2 14=12, X 2 22=2, X 2 23=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

X 1 11=6, X 1 12=3, X 1 13=9, X 1 21=3, X 1 23=1, X 1 24=12, 

X 1 33=2, X 1 35=12, X 1 41=12, X 1 52=12, X 2 11=6, 

X 2 13=3, X 2 14=12, X 2 22=2, X 2 23=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

X 1 11=6, X 1 12=3, X 1 13=9, X 1 21=3, X 1 23=1, X 1 24=12, 

X 1 33=2, X 1 35=12, X 1 41=12, X 1 52=12, X 2 11=6, 

X 2 13=3, X 2 14=12, X 2 22=2, X 2 23=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

X 1 11=6, X 1 12=3, X 1 13=9, X 1 21=1, X 1 23=3, X 1 24=12, 

X 1 31=2, X 1 35=12, X 1 41=12, X 1 52=12, X 2 11=6, 

X 2 13=4, X 2 14=11, X 2 22=2, X 2 24=1, X 2 25=12, 

X 2 31=12, X 2 42=12, X 2 53=12. 

In certain situations, two objectives are relevant in transshipment problems. Also, 

the goods transportation may not operate always directly among suppliers and 

customers. In such problems, it is possible to optimize the transshipment problem 

into two stages. The presented algorithm in this paper enables solving such 

problems more realistically. It can be used for determining all efficient extreme 

points. 

The main advantage of this approach is that the bicriteria two stage transshipment 

problem can be solved using the standard form of a transshipment problem at each 

iteration. 

From the application, decision maker will have all efficient extreme points and 

their related distributions. Therefore, he can choose any point which provides his 

policy. 

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algorithm for multi-objective transportation, assignment, and 

transshipment problems”, Life Science Journal, 9 (3): Page 1765 -177 


TRIBOLOGY OF HIGH SPEED MOVING MECHANICAL SYSTEMS FOR SPACECRAFTS - TRIBOLOGICAL ISSUES 

K. Sathyan 

Tribology of High Speed Moving Mechanical Systems for Spacecrafts - Tribological Issues 

K. Sathyan* 

E-mail: krishnan.sathyan@gmail.com 

* Department of Mechanical Engineering 

Prince Mohammed Bin Fahd University, Po Box:1664, Al-Khobar- 31952, KSA 

Tel.: +966 38498532; +966 505181702 

ABSTRACT 

Spacecraft regardless of size, type and purpose, usually contains a number of moving mechanical systems (MMS). Continual performance of these 

systems only can guarantee the intended functions that are essential for successful operation of the spacecraft. Most of the problems encountered with 

these moving systems are pertain to tribology. Space tribology is a subset of the lubrication field dealing with the reliable performance of satellites and 

spacecraft including the space station. Lubrication of space system is still a challenging task before the tribologists due to the unique factors 

encountered in space such as near zero gravity, hard vacuum, weight restriction and attention free operation. Ever since the space exploration, a 

number of mission failures reported emanate from bearing system malfunction. A bearing in a moving mechanical assembly can fail due to multiple 

reasons such as degradation of lubricant, loss of lubricant from the working zone by surface migration and evaporation, and retainer instability. Unlike 

yester years, space missions of today are planned to last for 30 years or more. To achieve such long-term missions, tribologically efficient moving 

mechanical systems are essential. This review briefs space tribology and tribological requirements of spacecraft moving mechanical systems. 

Keywords: spacecraft, momentum wheel, tribology, lubrication, attitude control 

INTRODUCTION 

More than 50 years have passed since the beginning of the space 

exploration. Still, malfunctioning of spacecraft components have been 

observed throughout the world. In many cases, these component 

failures lead to partial or total failure of the spacecraft mission. During 

these years, tremendous growth has been observed in the electrical, 

electronic and electromechanical components through disciplined 

design, standardization and quality assurance practices. This progress 

has helped in the miniaturization and hybridization of spacecraft 

systems and the development of cost effective spacecraft missions. 

However, notwithstanding the progresses made in the mechanical 

engineering, spacecraft designers are still striving to develop efficient 

mechanical systems that can cope with long-term requirements. During 

mid-1960’s mission life requirements were 3 to 5 years and by the mid- 

1970’s life requirements of 7 to 10 years were common [1]. But today, 

attention is focused on the development of subsystems for spacecrafts 

with longer mission duration of more than 30 years, a typical case 

being the space exploration initiative (SEI) of NASA [2]. These 

missions will require mechanical systems that operate for 30 years. 

These long life requirements bring a lot of challenges with them, 

especially in the area of moving mechanical systems. 

Spacecraft incorporate a wide variety of moving mechanical systems 

which must operate with total reliability in space environment. These 

moving systems can be broadly classified as high speed systems which 

include gyroscopes, momentum/reaction wheels etc., and low speed 

systems that encompass the hinges, scanners, solar array drive etc. The 

moving mechanical systems contain sliding or rolling contacts that are 

required to operate with least frictional power loss, in view of limited 

power availability on board the spacecraft. Each of these systems is 

designed to perform some definite task. For example, gyroscopes are 

used in the attitude control system (ACS) as an inertial sensor to detect 

the attitude error of the spacecraft with respect to a reference object 

(stars, sun, earth etc.). Similarly, momentum/reaction wheels are used 

in the attitude control system as actuators to correct the attitude error 

and maintain the spacecraft attitude. Thus attitude control can be 

defined as the process of achieving and maintaining a desired 

orientation of the spacecraft. This is vital in achieving the mission 

objectives. Since control and maintenance of spacecraft attitude is a 

continuous process, various elements of the attitude control system 

have to work continuously from the beginning to end of the mission. 

Moreover, high speed mechanical systems involved in this process are 

prone to degradation failure. In these systems, failures are mostly 

related to tribology. A number of mission failures are reported due to 

the tribological malfunction of attitude control systems. Skylab and 

Insat-1D are typical examples [3-5] and the most recent is the bearing 

failure in the control moment gyro (CMG) of the international space 

station on July 2002 [6]. Therefore, the development of high speed 

attitude control systems for the future requires advancement of 

tribology technology. Hence, by highlighting the tribological issues of 

spacecraft attitude control systems here, possible tribological solutions 

for the development of attitude control systems for future long-term 

applications are elaborated. 

SPACE TRIBOLOGY –OVERVIEW 

Tribology is defined as the science and technology of interacting 

surfaces in relative motion, or in other words, it is the study of friction, 

wear and lubrication. It is a truly interdisciplinary field that 

encompasses material science, chemistry, physics, mechanics, 

thermodynamics etc. The word “tribology” was introduced in 1966 by 



K. Sathyan 

“Department of Education and Science Report” from England [7]. 

However, man’s interest in the constituent parts of tribology is older 

than recorded history. It is evident from the invention of the wheel that 

reduced friction in translational motion. It is estimated that 

approximately one-third of the world’s energy resources utilization 

appear as friction in one form or another [8]. These frictional losses in 

terms of monetary losses to industries are enormous. With the evolution 

of this interdisciplinary branch of science, a systematic approach for the 

study of friction and methods to reduce its harmful effect on interacting 

surfaces are formulated. This has helped the current world to save 

considerable energy and thus money through good tribological design 

practices. 

Space tribology is a subset of the lubrication field dealing with the 

reliable performance of satellites and spacecraft (including the space 

station) [9]. In a spacecraft, there are a number of mechanisms that 

contain machine elements having interacting surfaces. The friction in 

these elements causes excessive wear and tear of the components which 

reduce the life and performance of the spacecraft. One of the major 

challenges a design engineer of spacecraft faces is the design of 

mechanical systems which consumes lowest electrical power. This 

amounts to a system design with lowest mechanical losses. This is 

possible only by reducing the frictional losses at the interacting surfaces 

through tribologically efficient design. Since the availability of power 

in a spacecraft is limited, its optimum usage will help in making the 

mission successful. The factor that complicates the space tribology is 

the space environment. Unlike terrestrial tribology, the presence of 

vacuum and extreme temperatures poses daunting challenges to the 

tribologists. The first challenge is to develop lubricants that can 

withstand these extreme conditions. Through concerted research over 

the years, a number of lubricants have been developed which have 

proved their suitability for extreme operating environments. The second 

challenge is to develop efficient lubrication technique to ensure the 

required performance and desired life. Through rigorous research, 

space tribologists have developed various lubrication techniques for 

different spacecraft mechanical systems. In spite of the tremendous 

progress made in the area of lubrication over these years, failure of 

spacecraft systems still persists. This shows that there is a considerable 

gap between the demand and availability lubrication technology. 

Figure 1 shows the growth of space technology, associated tribology 

demand and the solutions derived to cope with the demand. It is seen 

that the space technology over these years is steadily growing to fulfill 

the needs of the scientific and business world. At the beginning of the 

space exploration, spacecrafts were designed mainly to study the space 

environments and most of these spacecrafts were designed for shorter 

life. Later, in 1960’s with the advent of communication satellites 

(Telstar in July 1962 [10]), the mission life became critical. This long 

life requirement demanded long lasting spacecraft systems. During 

these periods, tribology was in its infant stage or even not known or 

developed. Consequently, the factor which decided the life of 

components of the spacecrafts is mostly mechanical failure owing to 

tribological malfunction. The demand for long lasting tribo-systems 

has grown up as the complexity of the spacecraft increased. Today, it 

has reached a state where missions are planned to last for decades, a 

typical example being the international space station (ISS). However, 

the frequent failures of moving mechanical systems in spacecrafts 

reveal that the growth of space tribology is lagging behind the demand. 

It is imperative to carry out concentrated research and development in 

space tribology. 

Fig.1. Growth of spacecraft technology, tribology demand and 

solutions 

The prime objective of the study of tribology is to understand the 

causes of friction and the means to reduce it. The effect of friction can 

by reduced by separating the surfaces in relative motion by interposing 

a third body that has a low resistance to shear so that the two surfaces 

do not sustain serious damage or wear. This third body is called 

lubricant and it can be a liquid, solid or gas. In a spacecraft there are 

mechanical systems that are lubricated either by liquid lubricants or 

solid lubricants. Most of the high speed systems such as gyroscopes, 

momentum/reaction wheels use liquid lubricants. All these systems are 

sealed to protect them from the space vacuum. Most low-speed systems 

like solar array drives, sensors, and antenna scanners use solid or semi 

solid lubricants. Since these systems are exposed to hard vacuum, 

liquid lubricants are not suitable due to their proneness to higher 

evaporation. In addition, the lubricants used in these systems must 

withstand exposure to radiation, electrons, protons etc. The nature and 

quantity of this flux is dependent upon the orbit [11, 12]. These 

requirements favor the use of solid lubricants. 

Solid Lubrication 

The solid lubricants used in spacecraft mechanisms come under three 

classes. These are soft metals, lamellar solids and polymers. Soft metals 

include gold (Au), silver (Ag), and indium (In). Lamellar solids include 

transition metal dichalcogenides, like molybdenum disulphide (MoS 2 ) 

and tungsten disulphide (WS 2 ). These compounds have a layered 

structure and low friction properties (typically


K. Sathyan 

in high friction. However, this method is still used in some components 

where friction is not so critical such as in clamps, release mechanisms 

etc. Vacuum deposition technique is used to give a thin uniform coating 

of lubricant to bearings used in precision mechanisms such as solar 

array drive, slip rings and brushes, scanner bearings etc. In this process, 

the film thickness can be accurately controlled. The film thickness is 

dependent on the surface roughness and cleanliness of the substrate. 

Therefore, before the coating process, the bearing surfaces are cleaned 

by the sputtering technique. Usually, the thickness of the lubricant film 

will be less than a micron. Sputtering and ion-beam techniques are used 

to give uniform coating. This method is widely used to plate MoS 2 and 

lead (Pb) ion on precision bearings that are exposed to hard vacuum. Of 

these two commonly used solid lubricants (MoS 2 and Pb [11, 13-15]), 

the lead ion has limited life in the presence of air due to the formation 

of oxides. Therefore the spacecraft systems with lead ion plated 

bearings are to be protected with inert gas during testing phase. In the 

space environment, these films show extremely low friction. Gold and 

silver are plated to tribological surfaces function as electrical 

conductors such as the slip rings and brushes in a solar array drive 

mechanism. 

Liquid Lubrication 

As mentioned above, most of the high speed systems used in spacecraft 

are lubricated by liquid lubricants. The primary advantage obtained 

with liquid lubricants is that the bearing surfaces separated by the 

hydrodynamic film of the lubricant, have virtually no wear, and thereby 

have potentially infinite lives. Depending upon the thickness of 

lubricant film present between the interacting surfaces, four well 

defined lubrication regimes are identified, such as hydrodynamic, 

elastohydrodynamic (EHD), mixed and boundary lubrication regimes 

[9,16-19]. These four regimes are clearly understood from the 

Stribeck/Hersey curve (Stribeck performed a series of journal bearing 

experiments in the early 1900's [20]. He measured the coefficient of 

friction as a function of load, speed, and temperature. Later, Hersey 

performed similar experiments and devised a plotting format based on a 

dimensionless parameter, ZN/P [21].), which shows the coefficient of 

friction as a function of dimensionless bearing parameter (ZN/P), where 

Z is the lubricant viscosity, N is the velocity and P is the bearing load. 

These regimes are depicted in Figure 2 [18]. A space bearing with 

liquid lubrication undergoes the last three regimes namely EHD, mixed 

and boundary before it fails due to lubricant starvation. The 

characteristics of these regimes are briefly presented here. 

Hydrodynamic lubrication: In hydrodynamic lubrication, the thickness 

of the lubricant film is sufficiently thick to separate the interacting 

surfaces. This will occur when the lubricant viscosity and or speed are 

sufficiently high and the load on the bearing is low. The film thickness 

will be greater than 0.25 µm and no metal to metal contact occurs. This 

kind of lubrication is not suitable for space bearing because it is not 

possible to store and supply such a high quantity of lubricant required 

for longer periods. 

Fig.2. Stribeck / Hersey curve [18] 

Moreover, the liquid lubricants are prone to contamination by 

evaporation, and this will have harmful effect on other components. For 

this reason, the space bearings are lubricated by minimum quantity and 

the bearing systems are hermetically sealed. 

Elastohydrodynamic lubrication (EHL): In EHL [19,22-24] the bearing 

pressure increases to a level where the lubricant viscosity provides 

higher shear strength than the interacting metal surfaces. Here, the 

lubricant is carried into the convergent zone approaching the contact 

area. As a result, the metal surfaces deform elastically in preference to 

the highly pressurized lubricant, which increases the contact area 

(Figure 3). In other words, the load is carried by the elastic deformation 

of the bearing material together with the hydrodynamic action of the 

lubricant. A bearing operating in EHD region shows an indefinite life 

with least friction torque (Figure 2). The most interesting practical 

aspect of the EHL theory is the determination of lubricant film 

thickness which separates the ball and the races. The generally used 

equation for calculating the film thickness is the one developed by 

Hamrock and Dowson [19]: 

0.68 

0.49 -0.073 -0.68k 

H 

min 

= 3.63 U 

s 

G W 1 - e 

[1] 

and 

H = min 

h 

min 

R x 

 

, [2] 

where, H min is dimensionless minimum film thickness, U s is the 

dimensionless speed parameter, G is the dimensionless material 

parameter, W is the dimensionless load parameter, k is the ellipticity 

parameter, h min is the minimum film thickness and R x is the effective 

radius. 

The effectiveness of EHL is described by the film parameter or λ ratio, 

which is the ratio of central film thickness at the hertz contact zone to 

the r.m.s surface finish of the rolling element surface; 

 

h min 

= 

1 

[3] 

2 2 2 

s r + s 

b 

 

 



K. Sathyan 

where, s r and s b are the r.m.s surface finish of races and balls. The EHL 

regime is characterized by λ ratio between 3 and 10 which corresponds 

to a film thickness between 0.1 and 1 μm. It has been pointed out that a 

full film can be obtained with no asperity contact only when λ > 3. If λ 

< 3, it will lead to mixed lubrication with some asperity contacts [22]. 

The concentrated research on EHL resulted in the identification of three 

subdivisions in EHL, namely starved EHL, parched EHL and 

transient/non - steady state EHL [25]. In starved EHL, the pressure 

build-up at the inlet contact region is low due to restricted oil supply. 

As a result the lubricant film will be thinner than calculated by EHL 

theory [22]. In parched EHL, the lubricant film is so thin that they are 

immobile outside the contact zone [26, 27] and this regime is 

particularly important for spacecraft systems bearings operating at high 

speeds. In the transient/non-steady state EHL, the load, speed and 

contact geometry are not constant with time. The theoretical behavior 

of this regime in point contact bearings is not well understood [25] but 

it is studied experimentally by Sugimura et al. [23]. 

Fig.3. Elastohydrodynamic lubrication 

Mixed lubrication: If the bearing pressure in an elastohydrodynamically 

lubricated bearing is too high or the running speed is too low, the 

lubricant film will be penetrated. The asperities of the bearing surfaces 

will come into contact and partial lubrication results. The behavior of 

the conjunction in a mixed lubrication regime is governed by a 

combination of boundary and fluid film effects [24]. The value of λ in 

this case is between 1 and 5. In spacecraft bearings mixed lubrication 

will occur when there is insufficient supply (starvation) of lubricant to 

the working zone. 

Boundary lubrication: In boundary lubrication, the interacting surfaces 

are not separated by the lubricant film. The lubricant film thickness is 

so narrow that direct metal to metal contact occurs. The coefficient of 

friction is high (0.15) and the resultant heat generation also high. The 

frictional characteristics are determined by the properties of the 

interacting surfaces and the lubricant film present. The high pressure 

and temperature at the contact surfaces causes the formation of a 

reactive film (called boundary film) which is capable of supporting the 

load without major wear or breakdown. To impart boundary lubrication 

properties, most space lubricant are processed with boundary additives. 

The commonly used inorganic additives are compounds of chlorine, 

sulfur, phosphorus and iodine [24]. The value of film parameter (λ) at 

boundary lubrication is less than 1 and the lubricant film thickness is 

less than 2.5 nm. The high speed space mechanism bearings are not 

preferred to operate in the boundary regime due to high friction. 

PROPERTIES OF LIQUID LUBRICANTS 

Since no single lubricant can meet the often conflicting requirements of 

various applications for liquids, hundreds of specialty lubricants have 

been developed for aerospace applications [28]. There are a number of 

factors to be considered while selecting a lubricant for space 

application such as operating temperature range, working environment, 

load on the bearings, speed of operation, bearing frictional torque etc. 

A space lubricant should have the following essential properties: 

Viscosity index: Since the system has to work over a wide temperature 

range (typically between 15 and 85 °C) the change in viscosity with 

temperature should be the minimum to maintain the EHD film. A space 

bearing is required to work with steady friction torque; otherwise the 

torque noise will act as a disturbance torque on the spacecraft. 

Therefore to maintain the viscous friction of the bearing constant at the 

working temperature range, high viscosity index lubricant is to be 

selected. 

Vapor pressure: The volatilization of lubricant contaminates the system 

and may have harmful effects; therefore the vapor pressure should be 

low in order to minimize losses by evaporation and to limit the 

pollution due to degassing. Figure 4 [25] shows the relative evaporation 

rates of various aerospace lubricants. 

Pressure–viscosity coefficient (α): The pressure-viscosity coefficient is 

important in determining the EHD film thickness at the ball-race 

contact inlet. It is observed that the fluid viscosity is an exponential 

function of pressure such that between the contacting surfaces in a 

loaded rolling bearing assembly, viscosity is likely to be 10,000 times 

its base value at zero pressure [29]. Also, from EHL theory, the 

lubricant with the largest α value should yield the thickest film at room 

temperature [25]. Since the bearings will subject to severe loads during 

the launch phase of the spacecraft, lubricants with high α values are to 

be selected. 

Creep: All liquid lubricants have a tendency to creep or migrate over 

bearing surfaces. It has previously been demonstrated by Fote et al. [30, 

31] that small temperature gradients cause a rapid and complete 

migration of oil films toward the regions of lower temperature. The 

migration was induced by capillary forces, temperature gradients and 

gravity. The creep is inversely related to lubricant’s surface tension, 

i.e., if the lubricant surface tension is low, there is more chance of its 

migrating from the working zone of the bearing. Hence, lubricants with 

high surface tension are selected for space application. 

Fig.4. Evaporation rates of various aerospace liquid lubricants [25] 



K. Sathyan 

There are a number of liquid lubricants that have been used in high 

speed moving mechanical systems. These lubricants fall under different 

classes based on their chemical structure such as mineral oils, silicon 

fluids, esters, synthetic hydrocarbons, perfluoropolyethers (PFPE) and 

silahydrocarbons. 

Table 1 [32] shows the property data of some of these lubricants. 

Mineral oils are natural hydrocarbons with a wide range of molecular 

weights. The paraffinic base oils are commonly used for space 

applications. These are available in a wide viscosity ranges, for 

example SRG-40 and SRG-60. Silicon lubricants were used in the early 

spacecrafts. Most of this oil has a very low vapor pressure and excellent 

low temperature properties. But it degrades quickly under boundary 

lubrication conditions [33], thus its application is discontinued in many 

apace systems. Esters are inherently good boundary lubricants and are 

available in a wide range of viscosities. Diesters and triesters are the 

commonly used lubricants. A series of esters are marketed by Nye 

Lubricants namely UC 4, UC 7 and UC 9 . The ISOFLEX PDP65, diester 

oil produced by Kluber Lubrication is used as a momentum wheel 

lubricant. Synthetic hydrocarbons are of two groups, polyalphaolefins 

(PAO) and multiply alkylated cyclopentanes (MACs). The PAO is 

made by oligomerization of linear α-olefins having six or more carbon 

atoms, for example: Nye 186A, 3001A. MACs are synthesized by 

reacting cyclopentadiene with various alcohols in the presence of a 

strong base [33]. The products are hydrogenated to produce the final 

products, which is a mixture of di-, tri-, tetra- or penta- alkylated 

cyclopentanes [9,25]. These lubricants are known as Pennzane ® and the 

Table.1. Properties of commonly used space lubricants [32] 

These are high density lubricants, and because of this property, yield 

EHD film thickness twice that of other lubricant having the same 

kinematic viscosity [25,35]. However, it has been reported that 

viscosity loss, both temporary and permanent, occurred under EHL 

conditions due to high contact pressure [34]. Silahydrocarbons are 

relatively new class of lubricant with great potential for use in space 

mechanisms. They are unimolecular species consisting of silicon, 

carbon and hydrogen and posses unique tribological properties. These 

are available as tri-, tetra- and penta- silahydrocarbons based on the 

number of silicon atoms present in their molecules. Silahydrocarbons 

are compatible with conventional lubricant additives. 

TRIBOLOGICAL ASPECTS OF MMS 

In this section, the tribological aspects of high speed MMS are 

reviewed. As mentioned previously, the high speed systems form part 

of the attitude control system (ACS) of a spacecraft. Most spacecrafts 

use momentum wheels, reaction wheels and control moment gyros for 

the attitude control process. Momentum/reaction wheels are spacecraft 

actuators used for control and stabilization of spacecraft attitude to the 

required level. A momentum wheel mounted in gimbals is known as 

control moment gyro (CMG). These are momentum exchange device 

that works by the principle of conservation of angular momentum. 

Conservation of angular momentum states that the angular momentum 

of a system without external torques is constant in the inertial frame. 

The satellite and the momentum wheel system have an angular 

momentum equal to the sum of individual angular momentum and it is 

constant at all times provided there are no external disturbances on the 

Lubricant 

Properties 

KG 80 

Mineral Oils 

SRG 60 

Kluber 

PDP 65 

Esters 

BP 135 

Silico 

n 

fluids 

Versilub 

e-F 50 

Synthetic Hydrocarbons 

Nye 

186A 

(POA) 

Nye 

3001A 

pennzane 

® SHFX- 

2000 

Fomblin 

Z-25 

PFPE 

Krytox 

143 AB 

Demnum 

Silahydrocarbons 

SiHC 1 , 

Type 1 

SiHC 2 , 

Type 2 

Viscosity, 

cSt 

@100 o C 9.44 15.5 16 14.6 15.75 14.6 49 10.3 15 12 

@ 40 o C 

Flash Point 

( o C) 

520 

(20 o C) 

77.6 73 

55 

(20 o C) 

52 103 127.5 108 159 85 500±25 94 79 

Index 101 106 235 128 146 130 137 335 113 210 170 169 

232 230 248 300 

Pour Point ( o C) -9 -12 -60 -45 -73 -48 -48 -55 -66 -43 -53 -50 -15 

Sp. Gravity 

( g/cc) 

Vapour 

Pressure 

(Torr) @100 o C 

Surface tension 

(mN/m) 

1x10 -6 

(20 o C) 

0.88 0.915 1.045 

0.85 

(15 o C) 

0.83 

(100 o C) 

0.85 

1.85 

(20 o C) 

10 -8 7x10 -4 10 -6 5x10 -8 2.4x10 -7 1.4x10 -10 1.3x10 - 

30 30 25 18.5 

8 

1.89 

1.5x10 - 

4 10 -5 

two types which are currently in use are SHF X1000 and SHF X 2000. 

The perfluoropolyether lubricants have been in use for over 30 years. 

This is a well-known ball bearing lubricant for the international space 

station [34]. These are made by polymerization of perfluorinated 

monomers. There a number of perfluoropolyether lubricants available 

for space applications such as Krytox , Fomblin , Demnum etc. 

satellite. The torque produced by changing the angular momentum of 

the wheel is used to turn the satellite to the required direction. Since the 

inertia of the satellite is large compared to that of the momentum 

wheels, a very precise control of the satellite orientation is possible 

with momentum wheels [32]. Typically, a momentum wheel consists of 

a flywheel which is driven by an electric motor (generally, a brushless 

dc motor) as shown in Figure 5 [36]. 



K. Sathyan 

Its precise rotation about a fixed axis is ensured by mounting it over a 

bearing unit consisting of a pair of high precision angular contact ball 

bearings. The normal operating speeds of momentum wheels are in the 

range of 4000–6000 rpm. The flywheel and the rotor of the motor are 

mounted on the bearing unit housing. The speed of the fly wheel is 

controlled through a drive electronics circuit. To protect from the 

outside environment, all these components are enclosed in a 

hermetically sealed metal casing purged with an inert gas. Usually the 

internal pressure is less than atmospheric, typically 375torr [32, 36]. 

Fig.5. Momentum wheel assembly [36] 

The bearing unit is the most critical component of a 

momentum/reaction wheels. The life and performance of the wheel 

greatly depend on the bearing unit. Unlike electronic circuits, it is not 

possible to design a momentum/reaction wheel with redundant bearing 

units. Therefore, utmost care is taken in the design, manufacturing and 

processing of bearing units. There are two different designs of bearing 

units available such as rotating shaft design and rotating housing 

design. Figure 6 [37] shows a typical rotating housing type bearing unit 

used in a momentum wheel [37]. The bearing unit is generally made of 

high quality steel (AISI 440C) to ensure high strength and dimensional 

stability. Usually the bearings and the bearing unit components are 

made of the similar material to eliminate the effects of thermal stresses, 

because in service the wheels are subjected to a wide range of 

temperatures. 

Fig.6. Momentum wheel bearing unit [37] 

The bearings typically used in a momentum wheel are of light series 

high precision angular contact ball bearings (ABEC - 9) with nonmetallic 

retainers (cages). Momentum wheels with retainerless ball 

bearings are also now available [38]. The size of the bearings is 

determined based on the angular momentum required. Typically, for a 

60 N.m.s wheel operating in a speed range 3000–6000 rpm, bearing of 

20 mm bore is common (104 size). Cotton based phenolic retainers are 

commonly used in these bearings. These retainers act as a primary 

source of lubricant when it is impregnated with the lubricant. A 

phenolic retainer for 104 size bearing, when properly impregnated and 

soaked for 60 days in oil, holds approximately 90mg of oil in its body. 

During impregnation and soaking, the oil penetrates into the cotton 

layer and is later available for lubrication. Also the metal parts of the 

bearing can hold approximately 15–20 mg of oil after it is centrifuged 

to the operating speed. Hence, altogether, about 100 mg of oil per 

bearing is available initially. With this initial lubrication, the bearings 

can perform up to 3–4 years normally, provided the retainer is running 

stable [32]. However, with retainerless bearings (full complement 

bearing), the retainer oil is absent and the bearing surface oil is about 

20 mg (addition of more balls) and the author have experience up to 13 

months at 5000 rpm with no extra oil added. However, the current life 

requirement for the wheels and other high speed space systems are 

more than 20 years or even up to 30 years [39]. According to Auer [40, 

41], ‘‘the ball bearing lubrication remains the principal life-limiting 

problem on momentum and reaction wheels’’. This tells us about the 

need for the development of efficient supplementary lubrication 

systems to achieve the future long-term space missions. Moreover, 

since it is not possible to service the spacecrafts once it is launched, insitu, 

remote lubrication systems are employed in momentum/reaction 

wheels. Also, the bearings are required to operate with the minimum 

frictional power loss, therefore it is preferred to operate in the 

elastohydrodynamic lubrication (EHL) regime. 

Tribological failures of high speed MMS are related to lubricant 

breakdown, loss of lubricant due to evaporation and surface migration 

(insufficient lubricant) and retainer instability. Lubricant breakdown 

failure occurs when the original liquid lubricant is chemically changed 

to solid friction polymer [42]. Kingsbury [43] has shown that the rate of 

lubricant polymerization is determined by the thickness of the EHD 

film - larger rate for thinner films and negligible for thicker films. Loss 

of lubricant in momentum/reaction wheels occurs mainly due to 

evaporation, surface migration and centrifugal action. The working 

temperature, which is also a function of bearing friction torque, causes 

the lubricant to evaporate. The oil loss by migration is induced by 

temperature gradients and capillary forces. It was demonstrated that a 

small temperature gradient leads to the rapid and complete migration of 

thin oil films to the colder regions [44]. The capillary migration 

describes the tendency of oil to flow along surface scratches and 

corners and is driven by pressure gradient in the radius of curvature of 

the oil–vapor interface. Retainer instability is the most dangerous mode 

of failure in momentum wheel bearings. It is characterized by large 

variation in bearing friction torque associated with severe audible noise. 

Uneven cage wear, lubricant degradation and insufficient lubrication 

are the prime causes for it. The retainer instability is related to number 

of factors like geometry and mass of the retainer, operating speed, 

lubricant quantity, etc., [45-47]. Momentum/reaction wheels with 

retainerless ball bearings will overcomes the most devastating problem 

observed in conventional bearings. Thus with the selection of proper 

lubricant and proven retainer design, lubrication remains the principle 

life limiting problem on high speed MMS. 



K. Sathyan 

CONCLUSION 

The scientific information provided here gives an overview of the 

tribological issues faced by the designers of spacecraft mechanical 

system. More than 50 years have now passed since the launch of the 

first spacecraft. Also, many decades of research and development have 

taken place after recognizing tribology as a special branch of 

engineering. Yet, tribological failures of spacecraft systems and 

resultant mission failures still persist. In many high speed moving 

mechanical systems failures are occurring mainly due to insufficient 

supply of lubricant. Currently, missions are planned to last for decades 

contrary to short missions of the past. Therefore, uninterrupted 

lubrication of these systems is a challenging task before tribologists. 

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Mirna Apriani, Ali Masduqi 

ABSTRACT 

The use of Iron in Peat Water for Fenton Process 

Mirna Apriani & Ali Masduqi, myrna_apriani@yahoo.com, masduqi@its.ac.id 

Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia 

The scarcity of water sources in the dry season caused peat water is still widely used as alternative water in peat area such as Kalimantan Island, 

Indonesia. Peat water contains organic matter, acid and iron (Fe 2+ ). For treating the peat water, advanced oxidation process (AOP) is an alternative 

treatment. AOP is an oxidation process that produces hydroxyl radical (OH*) which can oxidize the organic matter. One of AOP method is fenton 

process. This process uses Fe 2+ and hydrogen peroxide as oxidizer to produce hydroxyl radical. Fenton process can be run effectively at pH 2 to 4. 

Based on the characteristics of peat water, the aim of research is to examine the possibility using Fe 2+ in the peat water for fenton process. This 

research was conducted in a batch system with varying ratio H 2 O 2 /Fe 2+ at 3.5, 4, 4.5, and 5. The oxidation time is 150 minutes and measurement of 

iron and organic matter concentration was conducted every 30 minutes. The results of research show that iron in peat water can react with H 2 O 2 to 

produce OH* for removing the organic. It is time for 60 minute to oxidize in fenton process using peat water. 

Keywords: fenton process, peat water, hydroxyl radical 

INTRODUCTION 

Peat is formed from the accumulation of plant organic material on the 

condition of the stagnant swamp, so the process of decomposition is 

slow then there is the accumulation of organic matter. Organic matter in 

peat soil is a humic acid and fulvic acid. Peat soils are acid and contain 

cations such as Fe and Mn (Barchia, 2006). So that the peat water has 

high organic matter content, colour, are acid and contain high Fe. 

Indonesia has peat areas such as Kalimantan, Sumatera and Papua 

Island. 

Peat is the remaining of heap dead plants then decomposed by 

anaerobic and aerobic bacteria into a more stable component. It was not 

only organic matter which formed peat but also inorganic matter in 

small amount. The environment of peat deposition is always in the 

condition of saturation of water (more than 90%). Organic matter of 

peat-forming from plants in comparison with the different matter 

according to the decomposition level. Organic matter is composed of 

cellulose, lignin, bitumen, humus and others. Peat-forming elements is 

mostly composed of carbon, hydrogen, nitrogen and oxygen. In 

addition to the main elements are also other elements such as Al, Si, S, 

P and others (Sukandarrumidi, 1995). The humus process from plant 

residu into humus or peat called humification will result in humic acid 

and fulvic acid. Humic acids contain more aromatic compounds than 

the fulvic acids, fulvic acids are aliphatic compounds containing more 

than humic acid. Aromatic organic acids characterized by a number of 

phenolic-OH functional groups is high, while the aliphatic organic 

acids characterized by a number of high-COOH functional groups. Peat 

material with relatively high of lignin, contains of humic acids more 

than peat material which is relatively high cellulose content. Indonesia 

has tropical peat made from woody forest which contains a high lignin, 

while non-tropical peat materials are generally made of sphagnum with 

high of cellulose and hemicellulose content. The humus process from 

plant residu into humus or peat called humification will result in humic 

acid and fulvic acid. Humic acids contain more aromatic compounds 

than the fulvic acids, fulvic acids are aliphatic compounds containing 

more than humic acid. Aromatic organic acids characterized by a high 

number of phenolic-OH functional groups, while the aliphatic organic 

acids characterized by a high number of high-COOH functional groups. 

Peat material with relatively high of lignin, contains of humic acids 

more than peat material which is relatively high cellulose content. 

Indonesia has tropical peat made from woody forest which contains a 

high lignin, while non-tropical peat materials are generally made of 

sphagnum with high of cellulose and hemicellulose content (Barchia, 

2006). 

Water contains natural organic matter (NOM) as a result of the 

interaction between the hydrological cycle and the biosphere and 

geosphere. These interactions are responsible for the diverse nature of 

NOM as the organic content of a particular water body is dependent on 

the surrounding environments biogeochemical cycles. NOM is a 

complex mixture of organic material and has shown to consist of 

organics as diverse as humic acids, hydrophilic acids, proteins, lipids, 

hydrocarbons and amino acids. The range of organic components in 

NOM varies from water to water and seasonally, this consequently 

leads to variations in the reactivity of NOM with chemical disinfectants 

such as chlorine (Goslan et al, 2003 in Murray and Parsons, 2004). 

Humic substances (HS) mainly humic acids represent a major fraction 

of natural organic matter in ground and surface water and pose a variety 

of problems in treatment operations and distribution system. HS 

contribute to odor, color, taste as well as acidity problems in water 

supplies (Katsumata, 2008). 

Several studies of peat water treatment into clean water and drinking 

water have been carried out. By using a combination of alum coagulant, 

peat and lime that is able to neutralize the pH, the color removal 

efficiency reached 97.5%, 98.5% removal in turbidity and a decrease of 

90% organic matter (Karbito, 1999). The decreasing of organic content 

using ultrafiltration membrane with pre-treatment powdered activated 

carbon (PAC) which achieved an efficiency of 98.02% color re moval 

and 98.54% organic removal (Riduan, 2002). Combination of 

biological treatment using upflow anaerobic filter with physical 

processing using slow sand filter can reduce organic matter, color, 




turbidity, Fe and Mn, but only Fe that meets the requirements as clean 

water (Eri, 2009). 

Conventional treatment of humic acids can be done using coagulation 

process (Hendricks, 2005 and Wu et al., 2011), precipitation, filtration, 

ion exchange, adsorption using activated carbon and biological 

treatment (Wu et al, 2011). According Karbito (1999), coagulation to 

reduce the color and turbidity require high doses so it is difficult to 

apply at the household scale. According to Murray and Parsons (2004), 

the higher the dose of coagulant will increase the organic matter 

removal but sludge production will also increase which can cause new 

problems in its processing. 

According to the WEF (2008), Advanced Oxidation Process (AOP) is 

the oxidation process that produces reactive oxidants (such as the 

hydroxyl radical). According to Parsons (200 4), AOP is one of the 

water and waste water treatment technology, which utilizes an oxidant 

ability to process organic matter into a more simple form and harmless. 

Examples of carbon processed into carbon dioxide, hydrogen into 

water, nitrogen into nitrate and others. Processing using AOP has the 

ability to form strong oxidizing hydroxyl radicals which can oxidize the 

organic material is faster than using ozone. Oxidizing strength can be 

seen from the oxidation potential value that can be seen in Table 1. 

Table 1. Oxidation potential for various oxidator 

Oxidator 

Oxidation potential (V) 

Flourine 3.03 

Hydroxyl radical 2.80 

Atomic oxygen 2.42 

Ozone 2.07 

Hydrogen peroxide 1.78 

Permanganat 1.68 

Chlorine 1.36 

Processing using AOP can be processing using UV-light based 

applications (UV/H 2 O 2 and VUV), ozone-based applications (O 3 /H 2 O 2 , 

O 3 /UV, O 3 /H 2 O 2 /UV danO 3 /H 2 O 2 /TiO 2 ), heterogenous photocatalysis 

(TiO 2 /UV ), Fenton process, catalytic oxidation, electrochemical 

oxidation and oxidation ultrasound ( Matilainen and Silanpää, 2011) 

Fenton process is one of the AOP which the process using hydrogen 

peroxide oxidizer and a catalyst (iron salt) to produce hydroxyl radicals 

(OH*) (Parson, 2004; Jiang et al, 2010). Fenton process can be run 

effectively at pH 2-4. Fenton process does not use toxic materials, does 

not lead to residues and is simple technology (Parson, 2004). Fenton 

process consists of oxidation and coagulation that can occur in a single 

process through pH adjustment. Fenton process does not use toxic 

materials, does not lead to residues and simple technology (Wu et al, 

2010). Fenton process is the most inexpensive and easier compared to 

other process in AOP (Alaton et al, 2008). In an acidic environment, 

hydrogen peroxide and ferrous ion react in the following reaction: 

Fe 2+ + H 2 O 2 OH* + OH - + Fe 3+ [1] 

Organic + OH* H 2 O + products [2] 

According to Wu et al (2011), OH* reacts with organic material and 

oxidize Fe 2+ to Fe 3+ which can serve as a coagulant after the pH 

adjustment into above 6. The increasing of pH, will stop the oxidation 

process and continue to coagulation process. 

MATERIALS AND METHODS 

Peat water taken from Simpang Arja village, Rantau Badauh District of 

South Kalimantan - Indonesia. Sampling would be done at rainy season 

(April 2012). Using hydrogen peroxide solution (H 2 O 2 , 30%, w/w), the 

experiments were conducted in batch reactor using 1 L beaker glass. 

After hydrogen peroxide solution addition, the sample were stirred 

using the jar test with 50 rpm (Murray and Parsons, 2004) for 150 

minutes and measured iron and organic parameters every 30 minutes. 

Based on the analysis of the peat water samples characteristics is 

known that pH 3.4, the organic content of 63.2 mg / L and iron at 34 

mg / L. The initial pH value of sample was acid so it does not need pH 

adjustment. The iron concentration was used to determine the addition 

of hydrogen peroxide for each ratio H 2 O 2 /Fe 2+ variation. The optimum 

condition of H 2 O 2 /Fe 2+ to remove organic and iron is 3.5 – 4.5 (Wu et 

al, 2011) and 5 (Rohmatun et al, 2007). 

Analytical methods for initial characteristic and oxidation process using 

permanganate value test for organic parameter and for iron using 

spectrophotometric iron analysis. 

RESULT AND DISCUSSION 

The oxidation time was tested within the time interval range of 0 – 150 

min to determine whether the iron in peat water can be used for fenton 

process to oxidize the organic contaminant. The experiment used 34 

mg/L (0.61 mM) iron mM and the addition of 73.32 mL hydrogen 

peroxide (H 2 O 2 ) 2.14 mM, ratio H 2 O 2 /Fe 2+ is 3.5 for 1000 mL peat 

water. After the H 2 O 2 addition, the sample was stirred for 50 rpm. 

Analysing of iron and organic started after 30 minute stirring and 

continued every 30 minute. Fig 1 showed after 30 minute stirring iron 

and organic concentration is decrease. The percentage of iron 

decreasing are 73,42% for 30 minute ; 57,98% for 60 minute ; 70,57% 

for 90 and 120 minute ; 75,21% for 150 minute. The largest decreasing 

of iron is 75,21% for 150 minute. The decreasing iron value is in line 

with the decrease of organic. The percentage of organic decreasing are 

60% for 30 and 150 minute ; 55% for 90 and 120 minute ; 72,5% for 60 

minute. The largest decreasing of iron is 150 minute however the 

decreasing of organic for 150 minute is only 60% which smaller than 

for 60 minute (72,59%). So the optimum time for ratio H 2 O 2 /Fe 2+ 3.5 

was taken for 60 minute. 

Fig.1. The measurement of Fe and organic after the H 2 O 2 addition 

(Ratio H 2 O 2 /Fe 2+ = 3.5); (Fe 2+ 0.61 mM; H 2 O 2 2.14 mM) 

Fig 2 showed after 30 minute stirring, iron and organic concentration is 

decrease. The largest decreasing of organic to 34.76 mg/L after 120 

minute stirring and iron to 9.53 mg/L after 90 minute. For ratio 

H 2 O 2 /Fe 2+ is 4, the addition of H 2 O 2 2.44 mM for 1000 mL peat water 

is 83.80 mL. After the H 2 O 2 addition, the sample was stirred for 50 

rpm. The percentage of iron decreasing are 59,42% for 30 minute ; 

64,45% for 60 minute ; 71,98% for 90 minute ; 59,8% for 120 and 150 




minute. The largest decreasing of iron is 71,98% for 90 minute. The 

decreasing iron value is in line with the decrease of organic. The 

percentage of organic decreasing are 21,99% for 30 minute ; 36% for 

60 minute ; 37,5% for 90 minute ; 45% for 120 minute and 42,5% for 

150 minute. The largest decreasing of organic is 45% for 120 minute 

however the decreasing of iron for 120 minute is only 59,8% which 

smaller than for 90 minute (71,98%). So the optimum time ratio 

H 2 O 2 /Fe 2+ 4 was taken for 90 minute. 



Fig 4 showed after 30 minute stirring, iron and organic concentration is 

decrease. The largest decreasing of organic to 23.7 mg/L after 90 

minute stirring and iron to 8.06 mg/L after 90 minute. For ratio 

H 2 O 2 /Fe 2+ is 5.0, the addition of H 2 O 2 3.05 mM for 1000 mL peat water 

is 104.75 mL. The percentage of organic decreasing are 16% for 30 

minute ; 56% for 60 minute ; 62,5% for 90 minute ; 42,5% for 120 and 

50% for 150 minute. The largest decreasing of organic is 62,5% for 90 

minute. The percentage of iron decreasing are 51,16% for 30 minute ; 

72,71% for 60 minute ; 76,30% for 90 minute ; 60.51% for 120 minute 

and 59,78% for 150 minute. The largest decreasing of organic and iron 

happened in the same stirring time is 90 minute. So the optimum time 

ratio H 2 O 2 /Fe 2+ 5 was taken for 90 minute. 



The experiment using ratio H 2 O 2 /Fe 2+ is 4.5, the addition of H 2 O 2 2.75 

mM for 1000 mL peat water is 94.27 mL. After the H 2 O 2 addition, the 

sample was stirred for 50 rpm. Fig 3 showed after 30 minute stirring 

iron and organic concentration is decrease. The largest decreasing of 

organic to 20.54 mg/L after 60 minute stirring and iron to 9.08 mg/L 

after 30 minute. The percentage of iron decreasing are 73,3% for 30 

minute ; 70,18% for 60 minute ; 59,42% for 90 minute ; 63,74% for 

120 and 72,01% for 150 minute. The percentage of organic decreasing 

are 45% for 30 minute ; 87,5% for 60 minute ; 32,5% for 90 minute ; 

50% for 120 minute and 55,06% for 150 minute. The largest 

decreasing of iron is 73,3% for 30 minute however the decreasing of 

organic for 30 minute is only 45% which smaller than for 60 minute 

(87,5%). So the optimum time ratio H 2 O 2 /Fe 2+ 4.5 was taken for 60 

minute. 



From figure 1, 2, 3 and 4 showed that decreasing iron value is in line 

with the decrease of organic. The concentration of iron will be decrease 

as well as decreasing of organic concentration, means that the iron can 

react with hydrogen peroxide to produce hydroxyl radical to oxidize the 

organic. The optimum oxidation time happens after 60 minute for ratio 

H 2 O 2 /Fe 2+ 4 and 5 ; and 90 minute stirring for ratio H 2 O 2 /Fe 2+ 3.5 and 

4.5. In that condition, the decreasing of iron and organic concentration 

is the largest. 

CONCLUSION 

This paper provided the preliminary research on the removal organic in 

peat water with fenton process. Fenton process needs hydrogen 

peroxide oxidizer and a catalyst (iron salt) to produce hydroxyl radicals 

(OH*). The characteristic of peat water is acid, high organic and iron. 

This preliminary research conducted in the different ratio of H 2 O 2 /Fe is 

3.5; 4.0; 4.5; 5 without pH adjustment. To examine whether iron in peat 

water has potentially to used for fenton process, the sample only added 

H 2 O 2 based on the ratio. After a certain oxidation time, the 

concentration of iron is decrease in line with the decreasing of organic 

concentration. The iron in peat water can react with H 2 O 2 to produce 

OH* to remove the organic. For oxidation process in fenton process 

using peat water the minimum oxidation time is 60 minute. For further 

research, to treat the peat water using fenton process does not require 

the addition of iron salts. 




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151-156 


TRIBOLOGY OF HIGH-SPEED MOVING MECHANICAL SYSTEMS FOR SPACECRAFTS: LUBRICATION SYSTEMS 

OF BALL BEARINGS 

K. Sathyan 

Tribology of High-Speed Moving Mechanical Systems for Spacecrafts: Lubrication Systems of Ball 

Bearings 

K Sathyan, krishnan.sathyan@gmail.com 

* Department of Mechanical Engineering 

Prince Mohammed Bin Fahd University, Po Box:1664, Al-Khobar- 31952, KSA 

Tel.: +966 38498532; +966 505181702 

ABSTRACT 

The spacecraft attitude control system contains a number of moving mechanical systems (MMS). These include attitude error sen sors such as 

gyroscopes and actuators such as momentum wheels and reaction wheels. All these systems are designed to operate continuously till the end of the 

mission at varying speeds of several thousand rpm. The on-orbit performance of spacecrafts depends largely on the performance of the 

momentum/reaction wheels which, in turn, depend on the bearings used and its lubrication. The only component which undergoes wear in these 

systems are the ball bearings. Currently, the life cycle of spacecrafts are aimed to be around 20–30 years. However, the increases in size, complexity 

and life expectancy of spacecrafts demand advanced technologies especially in tribology and the development of more innovative lubrication systems 

for long-term operation. This part of the serial review presents an account of different types of lubrication systems commonly used in spacecraft highspeed 

moving mechanical systems. The features and working of active and passive lubrication systems are presented. The merits and demerits of each 

system are highlighted. 

Keywords: tribology, lubrication, momentum wheel, spacecraft, ball bearing 

INTRODUCTION 

It is well understood that no bearing can work indefinitely with the 

initial charge of lubricant given to it at the time of assembly. There will 

be progressive loss of lubricant from the bearing surface, and the rate is 

dependent on the operating conditions. In a spacecraft system bearing, 

it is not possible to provide lubricant in excess initially with a view to 

extending its life. To operate bearings with least frictional torque and 

torque variation, they have to work in the elastohydrodynamic 

lubrication ( EHL) regime. Therefore, bearings of high speed moving 

mechanical systems ( MMS) are centrifuged to remove the excess oil 

before assembling to the system. The bearing then contains the surface 

oil and the oil absorbed in the retainer pores. Thus, in order to achieve 

long mission life, supplementary lubrication is extremely important. 

The function of the supplementary lubrication system is to maintain 

right amount of lubricant at the bearing working surfaces to produce a 

thin film supporting the load. The thickness of the film should be 

sufficient to maintain the bearing in the EHL regime of lubrication. 

The ultimate aim of a spacecraft system designer is to minimize the size 

and weight of the system. Both these factors are critical in deciding the 

final weight and size of the spacecraft, which in turn influence the 

selection of launch vehicle. Therefore, optimum use of available space 

is appreciated. For this reason, the lubrication systems are enclosed 

either inside the bearing unit or inside the system enclosure. Currently, 

there are a number of different types of lubrication systems developed 

and used by different manufacturers for high speed MMS. However, 

according to the nature of operation, these lubrication systems used in 

high speed MMS can be broadly classified as passive lubrication 

systems and active lubrication systems. Various lubrication systems 

which come under these two categories are described in the following 

sections. 

PASSIVE LUBRICATION SYSTEMS 

The passive lubrication systems, also known as continuous lubrication 

system, supply lubricants continuously at a controlled rate irrespective 

of the requirement. In this class of systems, the lubricant is stored at 

ambient pressure in a lubricant reservoir located near the bearings. 

From the reservoir, the lubricant is fed continuously to the bearings at a 

predetermined rate. Most of these systems use centrifugal force due to 

the rotation of the bearing assembly to deliver the lubricant, while some 

use a transfer material such as cotton fiber that remains in touch with 

the bearing surface and lubricant in the reservoir. Passive type systems 

are simple in construction, but are difficult to control for the flow rate 

to the required level. Different techniques are used to control the flow 

rate in this type of lubricators. There are a number of designs of passive 

lubrication systems used today by different manufacturers of MMS for 

spacecrafts. The oozing flow lubricators (Kingsbury et al., 1999, 

Hashimoto, 2001, Jones et al., 1997, Singer, Gelotte, 1994), wick feed 

systems (Loewenthal et al., 1985), porous lubricant reservoirs (Sathyan, 

2003), the centrifugal lubricators (Sathyan, 2003, Sathyan et al., 2008, 

Sathyan et al., 2010) etc., come under this classification. 

AcademyPublish.org – Journal of Engineering and Information Technology Vol.2, No.2 39



K. Sathyan 

Oozing Flow Lubricator 

The ooze flow lubricator was invented by Fukuo Hashimoto 

(Hashimoto, 2001). The lubricator is fitted to the outer spacer of the 

bearing unit, the ends of which are formed as the bearing outer race. A 

set of precision turned helical grooves are made at the interface of the 

inner and outer part of the lubricator. The width of the groove is at least 

20 times the depth. The helical grooves run in the axial direction and 

deliver lubricant to each of the bearings. The rate of flow is controlled 

by the dimensions of the helical groove and the speed of rotation of the 

bearing shaft. The mathematically determined acceptable flow rate for 

the design was 5 – 50 µg/h. With the design goal of 20 µg/h, the 

expected life of the system was claimed as 15 years when operating at 

12 000 rpm. The space cartridge bearing system presented by 

Kingsbury et al. (Kingsbury et al., 1999), the oozing flow lubricator 

presented by Jones et al. (Jones et al., 1997), and Singer et al. (Singer, 

Gelotte, 1994) resembles the one mentioned above. Figure 1 shows the 

space bearing cartridge with oozing flow lubricator (Kingsbury et al., 

1999). 

through the bleed path. The oil coming out of the lubricator is guided to 

the bearings mounted on either side of the lubricator. 

Fig.2. A typical bearing unit assembly used in momentum wheels 

(Sathyan, 2003) 

Fig.1. Space cartridge bearing system with oozing flow lubricator 

(Kingsbury et al., 1999) 

Wick Feed Systems 

In wick feed lubrication system (Loewenthal et al., 1985) a cotton wick 

saturated with oil is continuously in contact with the bearings. The 

frictional contact causes small amount of oil to be deposited on to the 

contact surface. From this contact surface, oil migrates to the bearing. 

The other end of the wick is in contact with oil in a reservoir and it 

absorbs and maintains its saturation level. This system is used in early 

momentum wheels and with the advent of more robust systems, its use 

has been discontinued. The major disadvantage with this system is that 

the fibers in the wick may contaminate the bearing surfaces. 

Centrifugal Lubricator 

This is the most common type of lubricator currently used in 

momentum/reaction wheels and control moment gyros (CMG). In this 

lubricator, the lubricant (grease or oil) is filled in a cylindrical container 

and is assembled to the rotating part of the bearing unit (Figure 2). A 

lubricant bleed path is provided on the outer surface of the reservoir, 

through which the lubricant flows out. When the bearing unit is 

rotating, the lubricator attached to it also rotating at the same speed. 

The centrifugal force thus generated forces the lubricant to flow out 

The centrifugal lubricators need to be well characterized under the 

operating environments before it can be used in the actual system. The 

most promising advantage of this type of lubricator is that no external 

actuators are needed and it assures unattended long-term operation. It 

has the drawback of decreasing flow rate gradually, since the flow rate 

is proportional to the head of oil in the reservoir which is progressively 

diminishing with time. Some manufacturers use grease instead of oil to 

overcome the difficulty of flow control. But experience shows that the 

flow rate decreases drastically in this type of systems because of 

change in consistency of the remaining grease in addition to the 

decrease in the head of oil (Kingsbury et al., 1999). 

Figure 3 shows the centrifugal oil lubricator developed by Sathyan et 

al. (Sathyan et al., 2008, Sathyan et al., 2010, Sathyan et al., 2010, 

Sathyan, 2010). 

In this lubricator, the lubricant oil is filled in a metallic reservoir that 

contains an inner sleeve and an outer cup. The capacity of this reservoir 

is approximately 5000 cc. On the periphery of the outer cup, a small 

hole is drilled through which the lubricant flows out due to the 

centrifugal force. The diameter of this hole is about 100 µm. Since the 

pressure developed due to the rotation is sufficiently high, it is only a 

matter of hours to empty the reservoir through this hole. Therefore, to 

control the flow rate to the lowest possible, a restrictor mechanism is 

fitted on the reservoir directly above the hole. The flow is restricted by 

means of a micro orifice created on a metal foil of thickness 50 µm. 

The diameter of the micro orifice for the required flow rate can be 

obtained from the theoretical model of the lubricator. The flow rate 

from the lubricator (Sathyan, 2010) is given by: 

2 2 4 2 2 

r R3 R 

1 

q K 

8 

R3 R2 

 

where K is the flow coefficient (0.326), ρ is the density of the lubricant 

(kg/m 3 ), η is the dynamic viscosity of the lubricant (kg/m-s), ω is the 

angular speed (rad/s), r is the radius of the orifice (m), R 1 is the 

(1) 




K. Sathyan 

instantaneous radius of oil inner layer in the reservoir (m), R 2 is the 

radius at which oil enters the orifice (m) and R 3 is the radius at which 

oil leaves the orifice (m). In this case, R 2 and R 3 are constants and the 

difference between the two gives thickness of the orifice plate. q is the 

mass flow rate (kg/s). 

The coefficient K is obtained from the experimental and CFD 

simulation results. Thus, if the flow rate required is finalized, the flow 

area can be calculated. It is understood that the lubricant flow rate 

required maintaining continuous EHD film is of the order of 

micrograms/hour. The diameter of the control orifice required to obtain 

a flow rate of 10 µg/h is obtained using Eq. (1) is near to 2.8 µm. The 

orifice is created on the copper foil using a pulsed laser system. The 

lubricator assembly consists of two lubricators one for each bearing as 

shown in Figure 4 (Sathyan, 2010) The lubricator assembly can be 

mounted in the free spaces available between the bearings in the 

bearing unit as shown in Figure 2. The lubricant coming out of the 

lubricator flows to the bearings mounted adjacent to it. 

The predicted performance of the centrifugal lubricator is shown in 

Figure 5 (Sathyan, 2010). The diameter of the orifice is selected as 2.5 

µm and the operating speed and temperature are 5000 rpm and 23°C 

respectively. The temperature corresponds to the maximum that a 

momentum wheel experiences in a geostationary satellite. The lubricant 

selected for the calculation is KLUBER PDP-65; synthetic diester oil 

used in high speed MMS (Sathyan et al., 2008, Sathyan et al., 2010). It 

can be seen that the initial flow rate is about 6.5 µg/h and the flow rate 

at the 50 th year is about 4.36 µg/h. Also, the lubricator has consumed 

only 1920 mg oil, i.e. 40% of the total oil filled at the beginning, for 

lubricating the bearings. The interesting feature of this lubricator is that 

the flow rate can be varied by varying the quantity of lubricant filled in 

the reservoir. This lubricator is a strong candidate for future spacecraft 

requiring longer mission life. 

Fig.5. Predicted flow rate and total flow of the centrifugal lubricator 


Fig.3. Centrifugal oil lubricator (Sathyan, 2010) 

ACTIVE LUBRICATION SYSTEMS 

Fig.4. Centrifugal oil lubricator assembly (Sathyan, 2010) 

Active lubrication systems, also known as positive lubrication systems, 

supply a controlled amount of lubricant to the bearings when it is 

actuated by external commands. The command to actuate the lubricator 

is executed when a demand for lubricant arises. The demand for 

lubricant is indicated either by an increase in power consumption or by 

increase in bearing temperature as a result of increased bearing friction 

torque. Lubricant film thickness sensors are also used to measures the 

film thickness at the designated point. When the film thickness is less 

than a predetermined value, the lubricator is actuated and supplies 

lubricant. This type of systems contains a lubricant reservoir in which 

the lubricant is stored mostly under pressure. These systems are static 

and are generally mounted external to the bearing assembly. The flow 

from the reservoir is controlled by some mechanism that is actuated by 

external commands. There are arrangements to deliver the lubricant 

directly to the bearings. Different versions of positive lubrication 

systems are available with different actuators such as solenoid valves, 

electric heaters etc. The commandable oiler (Glassow, 1976) developed 

by the Hughes Aircraft Company, the positive lubrication system 

(PLUS) developed by Smith and Hooper (Smith, Hooper, 1990), the 

positive–pressure feed system proposed by James (James, 1977) etc., 

are examples of solenoid operated systems. The in-situ on demand 




K. Sathyan 

lubricator developed by Marchetti et al. (Marchetti et al., 2003, 

Marchetti et al., 2001), the static lubricant reservoir developed by 

Sathyan (Sathyan et al., 2010) etc., are examples of active lubrication 

systems using electric heater. The command lubrication system (CLS) 

developed by Sathyan et al., is of a different concept where the actuator 

is a stepper motor. 

Valve Operated Systems 

In valve operated positive lubrication systems, the lubricant is stored 

under pressure inside a leak proof container. The oil is pressurized by 

springs or by using compression bellows. The oil pressure is generally 

between 0.27 and 0.54 MPa. The oil reservoir and the bearing are 

connected by means of narrow steel tubes. One or more solenoid 

operated micro valves (normally closed) are connected to the line and 

near to the reservoir. The delivery end of the capillary steel tubes is 

placed adjacent to the bearings and is suitably shaped. 

The amount of lubricant delivered is determined by the duration of 

valve activation which is, depending on the oil viscosity and pressure, 

usually milliseconds or seconds. Figure 6 (Sathyan, 2003) shows the 

schematic of a solenoid valve operated active lubrication system 

(Sathyan, 2003). 

Here, the oil is stored under pressure using a metallic bellows. Two 

solenoid operated micro valves (V 1 and V 2 ) are used to control the 

lubricant supply to each bearing in the assembly. The capillary tubes 

are of 0.5mm internal diameter. The delivery end of the tubes are 

properly shaped and directed towards the outer spacer of the bearing 

unit which separates the bearings. 

The ends of the spacer which interface with the bearings are given a 

small taper of 0.5 degrees. When the valve is actuated, the oil flows 

through the capillary tube and injected in to the tapered surface of the 

rotating spacer. The centrifugal force causes the oil to flow axially into 

the bearings. It is also possible to deliver the oil directly to the bearings 

by placing the delivery tip of the capillary tube pointing the bearing. In 

such a case, there should be a standoff distance between the tip and the 

bearing surface. 

This distance is generally slightly less than the diameter of the oil drop 

formed at the delivery tip as shown in Figure 7 (Sathyan, 2003). In this 

case, when a drop is developed at the delivery tip, it comes in contact 

with the moving bearing retainer surface and is transferred to the 

retainer. The oil is distributed to the bearing contact through the 

retainer. At the tip of the capillary tube, anti-migration coating is 

provided which helps in forming droplets at the tip. 

Fig.6. Schematic of solenoid valve operated active lubrication system 


Fig.7. Method of oil delivery and position of delivery tip (Sathyan, 

2003) 

Electric Heater Operated Systems 

This type of system generally contains a lubricant reservoir made of 

porous material. Non-metallic isotropic porous materials such as 

sintered nylon, sintered polyimide etc. are generally used. The porosity 

and pore connectivity are well controlled by using spherical particle 

during sintering process. The porosity is typically between 15 and 30% 

by volume. When vacuum impregnated with oil, the reservoir carries 

oil sufficient to lubricate the bearings for many years. An electric heater 

(foil type) is attached to the reservoir. The reservoir with the heater is 

placed adjacent to the bearings. When the bearing oil film thickness 

falls below certain limit, the heater is operated for a specified time. The 

heater heats up the porous reservoir and oil flows out of the reservoir 

pores as a result of differential thermal expansion. The lubrication takes 

place by surface migration and vapor condensation. 

The in-situ on demand lubricator developed by Marchetti et al., 

(Marchetti et al., 2001, Jansen et al., 2002) consists of a porous material 

cartridge to which an electric heater is attached. The cartridge is 

impregnated with oil and is attached to the stationary race of the 

bearing. When the cartridge is heated, oil flows out of the cartridge and 

is migrated to the bearing surfaces due to the low surface tension of oil 

compared to the bearing metal. It is actuated when the bearing 

temperature increases due to higher friction, demanding lubricant. The 

system is evaluated using a spiral orbit tribometer and proved its 

feasibility to use in long-lived spacecrafts (Jansen et al., 2002). 

The static lubricant reservoir developed by Sathyan (Sathyan, 2003) 

consists of a porous material (sintered nylon) reservoir mounted on an 

aluminum sleeve and a foil heater is pasted inside the sleeve. The 

porosity of the reservoir material is about 30% by volume so that it 

carries sufficient amount of lubricant to support for the entire mission 

period. The reservoir assembly is mounted on the static part of the 

bearing unit. When the heater is turned on, the aluminium sleeve gets 

heated up and transfers the heat to the oil in the pores of the reservoir. 

Due to differential thermal expansion, oil flows out of the reservoir and 

forms a thick layer at the surface. A portion of the lubricant evaporates 

due to the temperature (about 80 °C maximum) and low pressure (the 

internal pressure of momentum/reaction wheels are less than 

atmospheric). The lubrication is effected by surface migration and 

vapor condensation. Figure 8 (Sathyan, 2003) shows the arrangement 

of static lubricant reservoir. The major drawback of this kind of system 




K. Sathyan 

is the delayed lubrication process owing to the delay in oil getting 

heated and being ejected out of the system. Moreover, the heater 

activation time or heater power should be progressively increased after 

each operation to eject the same quantity of oil. 

Fig.9. The command lubrication system (Sathyan et al., 2010). 

Fig.8. Arrangement of static lubricant reservoir (Sathyan, 2003) 

Fig.10. Command lubrication system delivering oil directly to bearing 

cage (Sathyan, 2003) 

The command lubrication system (CLS) developed by Sathyan et al. 

(Sathyan, 2003, Sathyan et al., 2010) consists of a metallic bellows, a 

micro stepping motor, a low friction ball screw, injection nozzle and 

capillary tubes. The stainless steel bellows act as the oil reservoir in 

which the oil is stored under ambient pressure. This pressure is usually 

the internal pressure of the momentum/reaction wheel or CMG, if it is 

placed inside the system, and is usually varies between 15 and 350 torr. 

The bellows is of compression type having a swept volume of 

approximately 1.5 cc, i.e., the difference between the normal state and 

fully compressed state. The micro stepping motor, which is the 

actuator, is a geared motor having a torque capacity of 130 mN-m and 

is driven through the drive electronics. The motor shaft is connected to 

the reservoir bellows through the ball screw. The high precision ball 

screw is of miniature type having low friction 3 mm screw. It is 

properly lubricated with space proven lubricant and protected from 

contaminants. One end of the screw is rigidly connected to the motor 

shaft. The housing/nut of the ball screw is attached to the bellows 

through the link. The ball screw converts the rotary motion of the motor 

shaft into liner motion and thus actuates the bellow. On the delivery 

end of the bellows, a nozzle is attached which connects the capillary 

tubes with the bellows as shown in Figure 9 (Sathyan et al. 2010). The 

stainless steel capillary tubes are of 0.5 mm in diameter and are suitably 

shaped to reach up to the bearings as shown in Figure 10 (Sathyan, 

2003). The delivery end of the tube which acts as the delivery nozzle is 

ground and squared and is coated with anti-migration film as shown in 

Figure 7. This coating will help in the formation of oil droplet by 

preventing spreading of oil around the nozzle tip. The reservoir is fully 

charged with lubricant before it is assembled with the drive motor. The 

total mass of the assembly is approximately 60 gm including lubricant. 

As mentioned previously, high speed MMS bearings are assembled 

with an initial charge of lubricant. Typically, in a momentum wheel 

bearing with phenolic retainer, the initial oil is about 60 to 80 mg. This 

initial oil is sufficient for normal operation up to three years and it will 

then start showing symptoms of abnormality indicating the demand for 

lubricant. In such situation, the drive motor of the CLS is actuated for a 

predetermined period of time to deliver oil to the bearings. When the 

motor shaft rotates, the ball screw attached to it also rotates. The 

housing/nut of the ball screw which is rigidly mounted on the bellow 

moves linearly and presses the bellow. As a result, the pressure of oil in 

the reservoir bellows increases and it flows out through the capillary 

tubes. At the delivery tip of the tube, oil forms a drop and when the size 

of the drop is sufficiently large, it touches the moving component of the 

bearing. It is to be noted that the tubes are routed through the stationary 

component of the bearing unit and so it is stationery. The set-off 

distance i.e., the distance between the nozzle tip and the rotating 

element of the bearing is determined from the size of the oil droplet. It 

was experimentally determined that the weight of a drop of oil (Kluber 

PDP-65 oil) is approximately 8 mg and the drop size is about 2.5 mm. 

Therefore, the set-off distance in this case is taken as 2 mm. The nozzle 

tip can be suitably located near the bearing depending on the design of 

the bearing unit to ensure oil discharge to bearings. 

The CLS need to be calibrated before it is being integrated to the 

system. Calibration is done to determine the actuation time required to 

deliver each drop of oil. The actuation time is depends on the rotational 

speed of the motor shaft and the pitch of the screw. The calibration data 

of a CLS is shown in Figure 11 (Sathyan et al., 2003). The test is done 

under a vacuum of 350 torr at 25 o C and the motor input is kept 

constant. During calibration, the motor is run for a specific duration 




K. Sathyan 

(typically 5 seconds each) and the oil discharge at the delivery tip is 

collected and weighed. It can be seen from the figure that the total 

discharge in 50 cycles is about 750 mg, which is only half of the swept 

volume, i.e. oil available for lubrication. It is estimated that the average 

loss of lubricant from the bearing of a momentum wheel is about 10 

mg/year (Sathyan et al., 2010). This shows that if a quantity slightly in 

excess of this amount is supplied every year, the bearing failure can be 

eliminated. Therefore, if one drop (8 mg) oil is supplied every six 

months or a maximum of three drops per year, the failure due to 

lubricant starvation can be completely eliminated. From the calibration 

data of the CLS, which shows that one operation of duration 5 seconds 

deliver approximately 15 mg, even if two operations of 5 seconds each 

are planned every year, this system would provide lubrication up to 25 

years. The amount oil discharge from the CLS can be varied by varying 

the duration of operation time. The oil discharge can be properly 

controlled by selecting suitable actuator motor, fine pitch ball screws 

and suitable size bellows. 

Fig.11. Measured oil discharge from CLS (Sathyan et al., 2010) 

Jansen, M. J., Jones, Jr. W. R., Pepper, S. V. Evaluation of an in-situ, 

liquid lubrication system for space mechanisms using a vacuum spiral 

orbit tribometer. In: NASA-TM-2002-2111683; June 2002. 

Jones, W. R. Jr., Shogrin, B. A., Kingsbury, E. P. “Long –Term 

Performance of a Retainerless Baring Cartridge with an Oozing Flow 

Lubricator for Space Application”. NASA Technical Memorandum 

107492, August 1997. 

Kingsbury, E.P., Hanson, R. A., Jones, W. R., Mohr T. W. Cartridge 

bearing system for space applications. In: Proceedings of the 33rd 

aerospace mechanisms symposium. NASA conference publication, vol. 

209259, 1999, 137–43. 

Loewenthal, S. H., Scibbe, H. W., Parker, R. J., Zaretsky, E. V. 

“Operating Characteristics of a 0.87 kW-hr Flywheel Energy Storage 

Module”. NASA Technical Memorandum 87038, August 1985. 

Marchetti, M., Jones, W. R. Jr., Pepper, S. V., Jansen, M. J., Predmore, 

R. E. “In-Situ, On-Demand Lubrication System for Space 

Mechanisms”. Tribology Transactions, Vol. 46, Issue 3, 2003, 452-459. 

Marchetti, M., Meurisse, M. H., Vergne, P., Sicreb, J., Durand, M. 

“Analysis of oil supply phenomena by sintered porous reservoirs”. 

Tribology Letters Vol. 10, No. 3, 2001, 163-170. 

Sathyan, K, Hsu, H.Y., Lee, S.H, Gopinath. K. Long-term lubrication 

of momentum wheels used in spacecrafts—An overview. Tribology 

International, 43, 2010, 259–267. 

CONCLUSION 

Tribological failures of spacecraft mechanical systems are often single 

point failures affecting entire mission. In many high speed moving 

mechanical systems failures occur mainly due to insufficient supply of 

lubricant. Currently, missions are planned to last for decades as 

opposed to the short missions of the past. Therefore, providing 

uninterrupted lubrication of these systems is a challenging task before 

the tribologists. To help tribologists in their design, an account of 

different types of lubrication system currently used in the space 

industry is presented. The centrifugal lubricator-a passive type 

lubricator, and the command lubrication system – an active type 

lubricator, presented here are two promising candidates for lubrication 

systems of the future long-term spacecrafts. 

REFERENCES 

Glassow, F. A. “Assurance of Lubricant Supply in Wet-lubricated 

Space Bearings”. Proc.10th Aerospace Mechanisms Symposium, 

NASA Technical Memorandum 33-777, 1976, 90-106. 

Hashimoto, F. “Ooze Flow Bearing”. United State Patent, Patent no: 

6290397, September.18, 2001. 

James, G. E. “Positive Commandable Oiler for Satellite Bearing 

Lubrication,”11 th Aerospace Mechanisms Symposium, NASA CP- 

2038, 1977, 87-95. 

Sathyan, K. Development of a centrifugal lubricator for long-term 

lubrication of momentum wheels used in spacecrafts. PhD thesis, 

University of South Australia; March 2010. 

Sathyan, K. Long-term lubrication systems for momentum wheels used 

in spacecrafts. MS thesis, Indian Institute of Technology Madras; 

September 2003. 

Sathyan, K., Gopinath, K., Hsu, H. Y., Lee S. H. “Development of a 

Lubrication System for Momentum Wheels Used in Spacecrafts”. 

Tribology Letters, 32, 2008, 99–107. 

Sathyan, K., Gopinath, K., Hsu, H.Y., and Lee, S.H., Development of a 

Positive Lubrication System for Space Application. Tribology Online, 

5, 1, 2010, 40-45. 

Sathyan, K., Gopinath, K., Hsu, H.Y., and Lee, S.H., Long-term 

Lubrication System for Space Application. Proceedings, the 2010 

International Conference on Innovation, Management and Services 

(ICIMS-2010), Singapore, Feb 26-28, 2010. 

Singer, H. B., Gelotte, E. “Design of a High-Speed Reliable Ball 

Bearing. Proc.28th Aerospace Mechanisms Symposium”, NASA Conf. 

Publ. 3260, 1994, 279-283. 

Smith, D. W., Hooper, F. L. “Positive Lubrication System”. Proc.24th 

Aerospace Mechanisms Symposium, NASA Conf. Publ. 3062, 1990, 

243 – 258. 


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