Study on the Durability of Thermally Sprayed WC...
Transcript of Study on the Durability of Thermally Sprayed WC...
Study on the Durability of Thermally Sprayed WC Cermet Coating under Rolling/Sliding Contact
September 2005
Department of Engineering Systems and Technology Graduate School of Science and Engineering
Saga University
DEWAN MUHAMMAD NURUZZAMAN
Study on the Durability of Thermally Sprayed WC Cermet Coating under Rolling/Sliding Contact
By
DEWAN MUHAMMAD NURUZZAMAN
A dissertation submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in the Department of
Engineering Systems and Technology, Graduate School of Science and Engineering,
Saga University
September 2005
Supervisor: Professor Akira Nakajima
Dedicated To My Parents
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Contents
Page no.
Abstract iv
List of Figures vii
List of Tables x
Nomenclature xi
1. Introduction
1.1 Preface 1
1.2 Rolling Contact Fatigue of Machine Elements 2
1.3 Surface Modification by Coatings and Surface Treatments 2
1.4 Surface Modification Techniques 6
1.4.1 Coating Deposition Techniques 6
1.4.1.1 Hard Facing 7
1.4.1.2 Vapor Deposition 8
1.4.1.3 Plating 9
1.4.2 Surface Treatment Techniques 9
1.4.2.1 Microstructural Treatments 10
1.4.2.2 Chemical Diffusion Treatments 11
1.5 Review of Applications of Thermally Sprayed Cermet Coating 12
1.6 Background and Objective of this Study 14
1.7 Structure of the Thesis 17
2. Experimental Procedure
2.1 Introduction 18
2.2 Experimental Details 18
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2.2.1 Testing Machine and Test Rollers 18
2.2.2 Experimental Conditions and Procedures 23
3. Theoretical Analysis
3.1 Introduction 25
3.2 Review of Theoretical Studies 25
3.3 Elastic-Plastic Analysis 27
4. Durability of WC Cermet Coating under Rolling/Sliding Contact
4.1 Introduction 29
4.2 Experimental Details 30
4.3 Results and Discussion 32
4.3.1 Comparison of Surface Durability 32
4.3.2 Changes in Surface Profile 34
4.3.3 States of Oil Film Formation and Friction 35
4.4 Elastic-Plastic Analysis 40
4.5 Conclusion 45
5. Effect of Substrate Surface Finish on Durability of WC Cermet Coating
5.1 Introduction 47
5.2 Experimental Details 48
5.3 Results and Discussion 49
5.3.1 Comparison of Surface Durability 49
5.3.2 States of Oil Film Formation 53
5.4 Elastic-Plastic Analysis 54
5.5 Conclusion 60
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6. Rolling Contact Fatigue Strength of WC Cermet Coating under Partial EHL
Conditions
6.1 Introduction 62
6.2 Experimental Details 63
6.3 Results and Discussion 63
6.3.1 Comparison of Surface Durability 63
6.3.2 States of Oil Film Formation and Friction 69
6.4 Elastic-Plastic Analysis 71
6.5 Conclusion 78
7. Concluding Remarks and Subjects for Future Research 80
Acknowledgement 84
References 86
Appendix A Formulations of Oil Film Thickness, Load and Oil Film Parameter 92
Appendix B Theoretical Basis of Line Loading of an Elastic Half-Space 95
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Abstract
Much of the tribological research is commercially oriented and modern technology is
continually demanding low friction and high wear-resistant materials in order to modify the
surface characteristics for the purpose of improving the rolling contact fatigue strength of
contact machine elements such as rolling-contact bearings, gears, traction drives, cams and
tappets. In recent years, the quality and reliability of thermally sprayed coatings have been
improved remarkably to satisfy the growing needs of the market for high wear resistance of
engineering components. Among the cermet coatings, the most attractive proved to be the
hard coatings of tungsten carbide (WC) based cermets because of its excellent tribological
properties such as wear resistance and sliding performance. Substrate surface finish and
substrate material are very important for the degree of adhesion of cermet coating to the
substrate which in turn may have significant effects on the rolling contact fatigue life of
machine elements. Therefore, the effects of substrate surface finish and substrate material on
durability of thermally sprayed WC-Cr-Ni cermet coating were investigated experimentally
and theoretically. The effects of friction, contact pressure, coating thickness and mating
surface roughness on the durability of cermet coating were also investigated. These
investigations and the obtained results are given briefly in the following steps:
First, surface durability of thermally sprayed WC-Cr-Ni cermet coating in lubricated
rolling with sliding contact conditions was examined using a two-roller testing machine. The
coating was formed onto the axially ground, blasted and circumferentially ground roller
specimens made of a thermally refined carbon steel or an induction hardened carbon steel by
means of the high energy type flame spraying (Hi-HVOF) method. The WC cermet coated
roller finished to a mirror-like condition was mated with the carburized steel roller without
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coating having a surface roughness of Ry=3.0~5.0µm. In the experiments, a maximum
Hertzian stress of PH=0.6 or 0.8GPa was applied for the thermally refined carbon steel roller
and PH=1.4GPa was applied for the induction hardened carbon steel roller in line contact
condition. As a result, it was found that in the case of thermally refined steel substrate, the
occurrence of flaking was remarkably restrained when the substrate was axially ground,
while the durability of coated roller was lowered with blasted or circumferentially ground
substrate. The life to flaking of WC cermet coated roller had a tendency to be prolonged as
the coating thickness increased. In the case of induction hardened steel substrate, the coated
rollers exhibited a longer life compared with the thermally refined steel substrate, and the
durability or the life to flaking showed a little sensitivity to the substrate surface finish. It was
also confirmed that durability of coated steel roller is much higher than that of steel roller
without coating. Theoretical calculations revealed that rough substrate surface performs
better than smooth substrate surface to improve the durability of coated roller when the
coating thickness becomes thin in the lower hardness substrate such as thermally refined steel.
Second, WC-Cr-Ni cermet coating of 60 to 210µm in thickness was formed onto the
axially ground, blasted, and circumferentially ground roller specimens made of a thermally
refined carbon steel or an induction hardened carbon steel. In the experiments, WC cermet
coated steel roller was mated with the carburized steel roller without coating having a surface
roughness of Ry=0.1~0.4µm and a maximum Hertzian stress of PH=1.0 to 1.4GPa was
applied in line contact. In the case of thermally refined steel substrate, the coating on the
circumferentially ground substrate generally showed a lower durability compared with that
on the axially ground substrate or blasted substrate, and this difference appeared more
distinctly as the coating thickness decreased. On the other hand, the induction hardened steel
substrate roller showed a higher durability, and the effect of substrate surface finish was
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hardly recognized. Theoretical analysis revealed that in the case of thermally refined steel
substrate, axially ground substrate model performs better than the circumferentially ground
substrate model in order to improve the durability of WC cermet coating when the coating
thickness decreases and flaking of coating is easy to occur in the vicinity of the interface
layer when the substrate surface is circumferentially ground and frictional coefficient is high.
Third, rolling contact fatigue strength of WC-Cr-Ni cermet coating was investigated under
partial EHL condition (Λ<1). In the case of thermally refined steel substrate, depending on
the mating surface roughness and substrate surface finish, significant differences in the
durability of coated roller were found. Theoretical analysis revealed that in the case of low
hardness substrate, Hertzian stress and frictional coefficient play a dominant role in the
distribution of plastic strain when the substrate surface is circumferentially ground. These
theoretical results suggest that in the case of low hardness substrate, flaking of WC cermet
coating is very easy to occur in the vicinity of the interface layer if the substrate surface is
circumferentially ground. Moreover, it is concluded that high hardness substrate is effective
to improve the durability of WC cermet coating and these theoretical results are agreed well
with the experimental results.
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List of Figures
Page No.
Fig. 2.1a Two-roller testing machine 19
Fig. 2.1b Main part of the testing machine 19
Fig. 2.2 Test rollers 20
Fig. 2.3 Substrate surface before coating 21
Fig. 2.4 Cross-section of sprayed coating 21
Fig. 2.5 Observation of WC-Cr-Ni cermet coating and its component particles 22
Fig. 2.6 Cross-sections of sprayed coating (Sections perpendicular to roller axis) 23
Fig. 3 Model for finite element method (FEM) analysis 28
Fig. 4.1a Effects of substrate surface finish and substrate material on life to flaking (Thickness≈60µm) 32 Fig. 4.1b Effect of mating surface roughness on life to flaking
(Induction hardened steel: Thickness≈60µm, PH=1.4GPa, s=-28.0%) 33 Fig. 4.2 Profile curves of mating surfaces before and after running (PH=1.4GPa, s=-28.0%, RyF= 4.0µm) 34 Fig. 4.3 Effects of substrate surface finish and substrate material on states of oil film formation between rollers (Eab=0mV:contact, 15mV:separation, Thickness≈60µm) 36 Fig. 4.4 Views of contacting surfaces (Test AA-2: PH=0.8GPa, s=-14.8%) 36
Fig. 4.5 Views of contacting surfaces (Test BC-3: PH=1.4GPa, s=-28.0%) 37
Fig. 4.6 States of oil film formation between rollers: Comparison of with and without WC cermet coating (Eab=0mV:contact, 15mV:separation, Thickness≈60µm) 38
Fig. 4.7 Effect of substrate surface finish and substrate material on changes in coefficient of friction at the initial stage of running (Thickness≈60µm) 39 Fig. 4.8 Changes in coefficient of friction at the initial stage of running:
Comparison of with and without WC cermet coating (Thickness≈60µm) 39 Fig. 4.9a Smooth substrate surface 40
Fig. 4.9b Rough substrate surface 40
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Fig. 4.10a Effects of smooth substrate surface and rough substrate surface on residual stress 42
Fig. 4.10b Effects of smooth substrate surface and rough substrate surface
on plastic strain 42 Fig. 4.11a Effect of substrate material on residual stress 44 Fig. 4.11b Effect of substrate material on plastic strain 44
Fig. 5.1 Effect of substrate surface finish on life to flaking (Thermally refined steel substrate) 50 Fig. 5.2 Effect of substrate material on life to flaking 51
Fig. 5.3 External views of flaked surfaces 52
Fig. 5.4 Sectional view of flaked part (AC-2 D, Circumferential direction) 52
Fig. 5.5 Depth of flaking (Thermally refined steel, s=-14.8%) 53
Fig. 5.6 Oil film formation between rollers (Eab=0mV: Contact, 15mV: Separation) 54
Fig. 5.7a Circumferentially ground model 55
Fig. 5.7b Axially ground model 55
Fig. 5.8 Effect of coating thickness on residual stress σx 57
Fig. 5.9 Distributions of residual stress σx 57
Fig. 5.10 Effect of coating thickness on equivalent plastic strain εpav 58
Fig. 5.11 Distributions of equivalent plastic strain 59
Fig. 5.12 Distributions of equivalent plastic strain εpav along the interface layer 60
Fig. 6.1 Effect of mating surface roughness on life to flaking (Thermally refined steel, Thickness≈60 µm) 66
Fig. 6.2 External views of flaked surfaces 67
Fig. 6.3 Depth of flaking (Thermally refined steel: s=-14.8%, Thickness≈60µm) 67
Fig. 6.4 Profile curves of mating surfaces in axial direction 68
Fig. 6.5 Oil film formation between rollers (Thermally refined, Eab=0mV: Contact, 15mV: Separation) 69 Fig. 6.6 Changes in coefficient of friction (Thermally refined) 70
Fig. 6.7a Circumferentially ground model 72
Fig. 6.7b Axially ground model 72
Fig. 6.8 Distributions of residual stress σx (Low hardness substrate) 74
Fig. 6.9 Effect of substrate hardness on residual stress σx 74
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Fig. 6.10 Distributions of equivalent plastic strain εpav (Low hardness substrate) 76
Fig. 6.11 Effect of substrate hardness on equivalent plastic strain εpav 76
Fig. 6.12 Distributions of equivalent plastic strain εpav along the interface layer 77
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List of Tables
Page No.
Table 4.1 Summary of experiments and main results 31
Table 4.2 Material parameters 41
Table 5.1 Summary of experiments and main results 49
Table 5.2 Material parameters 56
Table 6.1 Summary of experiments and main results 64
Table 6.2 Material parameters 73
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Nomenclature
RCF rolling contact fatigue
PVD physical vapor deposition
CVD chemical vapor deposition
HV hardness Vicker’s
HVOF high velocity oxy-fuel
Hi-HVOV high energy type flame spraying
s slip ratio
Ry maximum surface roughness
ν kinematic viscosity, mm2/s
α pressure-viscosity coefficient, GPa-1
EHL elasto-hydrodynamic lubrication
hmin theoretical EHL minimum oil film thickness
Λ oil film parameter
N number of cycles
p(x) Hertzian contact stress
f(x) tangential traction
PH maximum Hertzian stress
x x-coordinate of the contact load
y distance along the Y-axis
x0 x-coordinate of the center of the contact load
b half-width of the Hertzian contact
µ frictional coefficient
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Eab voltage recorded on chart, mV
FEM finite element method
E Young’s modulus, GPa
ν Poisson’s ratio
sY yield stress, MPa
k shear yield stress, MPa
H tangent modulus, GPa
σx residual stress, GPa
εpav equivalent plastic strain
R reduced radius of the contacting solids
G material parameter
U speed parameter
W load parameter
E ′ reduced elastic modulus, GPa
P applied load, N
γ specific gravity of the lubricant
u average surface speed of the contacting solids, mm/s
0η lubricant viscosity at atmospheric pressure, Pa.s
xzzx τσσ ,, stress components
xzzx γεε ,, strain components
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Chapter 1
Introduction
1.1 Preface
A wide variety of engineering components can either deteriorate progressively or fail
catastrophically through surface-related phenomena. Any loss of surface material from one or
both surfaces when the contacting surfaces are subjected to relative motion is known as wear.
Wear costs a lot of money and it is the major cause of material wastage and loss of
mechanical performance of machine elements and any reduction in wear can result in
considerable savings (1).
Wear takes place at the surface and the near-surface. Improving the property of surfaces is
the current trend for solving today’s wear problems, rather than the development of new
wear-resistant bulk materials. Therefore, it is the goal to design a system involving unwanted
mechanical action on a surface that causes material removal. To protect surfaces from
deterioration in their use environment, it is aimed at tailoring the properties of contact
surfaces of engineering components such as rolling-contact bearings, gears, cams and tappets
to improve their function. Therefore, to altering the surface characteristics (superior to those
of the bulk material) for better use properties in the applications involving wear, surface
engineering is the most promising way to obtain higher serviceability in contacting machine
elements (2).
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1.2 Rolling Contact Fatigue of Machine Elements
Rolling contact fatigue (RCF) is a significant factor and is responsible for the failure of
machine elements such as rolling element bearings, gears, cams and tappets and may be
defined as cracking, or pitting, or spalling/flaking limited to the surface or near-surface layer
of the components under repeated rolling/sliding contact. The fatigue failure may be surface
or subsurface originated (3). Prior to the fatigue life (which may be hundreds, thousands, or
even millions of cycles), negligible wear takes place, which is in marked contrast to the wear
caused by an adhesive or abrasive mechanism, where wear causes a gradual deterioration
from the start of running. Therefore, the amount of material removed by fatigue wear is not a
useful parameter. Much more relevant is the useful life in terms of the number of revolutions
or time before fatigue failure occurs (4).
There is an increased demand for improved life, reliability and load bearing capacity of
bearing materials and future applications will demand their use in more hostile environments.
In order to achieve better use properties of the materials, surface modification technologies
are going with a remarkable progress for the purpose of improved rolling contact fatigue life
of machine elements.
1.3 Surface Modification by Coatings and Surface Treatments
Principal machine elements such as rolling-contact bearings, gears, traction drives, cams and
tappets are required to operate occasionally under severe tribological and environmental
constraints such as high surface speed, high corrosion environments, high operating
temperatures and high load conditions. Thus the surface failure such as pitting or
spalling/flaking occurs. In order to modify the surface characteristics for the purpose of
improving the rolling contact fatigue strength of contact machine elements, not only various
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coating deposition techniques such as thermal spraying, physical vapor deposition, chemical
vapor deposition and electrochemical deposition but also surface hardening processing or
surface treatment technique such as induction hardening, flame hardening, carburizing, and
nitriding are applied to the machine elements (4).
State-of-the-art technology of surface modification treatments modifies the contact
surface of machine elements physically and/or chemically and gives the functions such as
low friction, high abrasion resistance, resistance to corrosion and high temperature oxidation,
fatigue resistance and high scuffing/galling resistance, is making remarkable progress.
Although it is very difficult to select the optimal surface modification treatment according to
the purpose of usage, some techniques are used for the purpose of reducing the friction and
wear and consequently, the rolling contact fatigue life is improved.
Coatings are wear resisting materials and can be classified as hard coatings that exhibit
moderate friction but extremely low wear and soft coatings that exhibit relatively low friction
but relatively high wear. A brief description of some important hard and soft coatings is
given below.
Hard Coatings
Hard coatings have found extensive use in highly loaded applications to reduce wear.
Coatings of ferrous and nonferrous metals, intermetallic alloys, ceramics, and cermets
provide good wear resistance owing to their inherent high hardness. These coatings, ranging
in thickness from a fraction of a micrometer to several millimeters, can be applied by a
variety of deposition techniques, such as electrochemical deposition, thermal spraying,
physical vapor deposition, and chemical vapor deposition.
Among metals, nickel is the most widely used coating after hard chromium. Compared
with chromium, hardness of nickel is relatively low, but it has good mechanical strength and
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ductility, is a good conductor of heat, and has good resistance to corrosion and oxidation.
Coatings of ferrous based alloys (steels and cast irons) are used where heavy wear is
encountered, under conditions that impose mechanical and thermal shock. They are used for
corrosion and wear resistance. Cobalt- and nickel-based alloy coatings are superior in
hardness (wear resistance) at elevated temperatures and corrosion- and oxidation-resistant (5).
Ceramics are inorganic nonmetallic materials as opposed to organic (polymers) or
metallic materials. Another class of ceramic materials is known as cermets, consisting of a
metal or alloy and a ceramic intimately bonded together. The use of ceramics and cermets as
structural materials offers many advantages over metals and alloys such as high strength-to-
weight ratio, high stiffness-to-modulus ratio, high strength at elevated temperatures, and
resistance to corrosion. They are also economical and readily available (4). Some ceramics,
such as carbides, nitrides, borides, silicides, and oxides of most refractory metals with very
high melting points, appear to be ideal wear-resistant materials in a variety of tribological
situations, provided that their strength and toughness are acceptable for the application (6-10).
Generally, ceramics and cermets are much harder than metals and alloys, so they are
potentially abrasion-resistant. Thus ceramics and cermets are used primarily in applications
requiring high wear resistance under extreme operating conditions (high pressure, high
sliding velocity, and/or high temperature). Ceramics are chemically inert and they are
chemically stable in air at high temperatures. However, they are brittle and fail readily as a
result of mechanical or thermal shock. Engineering uses of ceramics have tended to
emphasize their wear-resistant and refractory properties at the expense of poorer thermal
shock resistance and low thermal conductivity. Ceramics are expensive to fabricate to good
dimensional tolerances and the superior properties can be achieved from improved
fabrication techniques (11-13).
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Soft Coatings
Coating used for solid lubrication, known as soft coatings, are produced by bonding loose
powder in a binder material, electrochemical deposition, and various physical vapor
deposition processes. Resin-bonded coatings are extensively used as solid lubricants for
many industrial applications. Solid powders such as MoS2 and graphite are bonded with
polymers and applied to clean or pretreated surfaces by spraying, dipping, or burnishing.
Generally, the bonded solid lubricant coatings are stable at temperatures up to about 2000C
(5).
Polymer coatings are important tribological materials because of their self-lubricating
properties, excellent wear and corrosion resistance, high chemical stability, high compliance,
high capacity for damping vibrations or for shock resistance, and low cost. They can be used
in unlubricated applications, unlike metals and nonmetals. Polymers are chemically inert and
thus are preferred in corrosive environments and can perform in operating temperatures
generally up to about 2000C (5).
The soft metal coatings, such as Ag, Au, Pb and Sn are applied by electrochemical
deposition and various physical vapor deposition processes. These coatings are particularly
valuable at very high temperatures and under severe environmental conditions. Gold and
silver coatings are used as lubricants in high-performance jet engines and high-speed
machines operating under lightly loaded conditions (4).
Surface Treatments
Surface treatments provide another approach to tailoring the surface characteristics of bulk
materials for tribological applications. These processes involve heating materials in reactive
or nonreactive atmospheres and result into microstructural changes and/or the formation of
chemical compounds only on the top layer of the material. Surface treatment processes do
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not produce coating-to-substrate interfaces as found in coatings. Many of the surface
treatment techniques can be applied very economically to large and intricate components
with thick transformed layers and are preferred over coatings for cost reasons. The surface
treatments are widely used mostly for ferrous-based materials. Surface treatments are
generally used to increase the surface hardness in order to improve the wear resistance (2).
1.4 Surface Modification Techniques
Many coating deposition and surface treatment techniques are available for the modification
of surface characteristics in order to improve the tribological performance of machine
elements. The effectiveness (load-carrying capacity, wear resistance, and coefficient of
friction) of coatings and surface treatments depends on the particular surface modification
technique. Selection of the coating deposition or surface treatment technique depends on the
functional requirements, shape, size and metallurgy of the substrate, availability of the
coating material in the required form, adaptability of the coating material for the technique,
level of adhesion desired, availability of coating equipment, and cost. Moreover, coating
deposition and surface treatment techniques must be compatible with the substrate (4).
1.4.1 Coating Deposition Techniques
A number of coating deposition techniques are available in tailoring surface characteristics
for tribological applications. They are mainly divided as hard facing, vapor deposition and
plating (5). A brief description of some important and most popular coating deposition
techniques is as follows:
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1.4.1.1 Hard Facing
Hard facing is used to deposit thick coatings (typically 50 µm or thicker) of hard wear-
resistant materials by thermal spraying and welding. In brief, these processes are described as
follows:
Thermal Spraying
The thermal spraying process is one of the most versatile methods available for deposition of
coating materials. Thermal spraying process is used to deposit practically any material and is
preferred for applications requiring hard coatings applied with minimum thermal distortion
of the workpiece. Thermal sprayed coatings are used extensively in various applications
requiring resistance to wear and corrosion. In thermal spraying, coating material is fed to a
heating zone where it becomes molten and then is propelled to the pretreated base material,
which is generally water cooled. Although the temperature of the molten particles striking the
base material is several hundred degrees Celsius, the base material remains below 2000C.
The thermal energy necessary to melt the spraying material can be produced by a flame
created by combustion gases. Substrates for thermal spraying need to be preroughened in
order to improve coating adhesion (5).
Welding
Welded coatings can be applied to substrates which can withstand high temperatures
(typically > 7500C) and are used to deposit mostly metals and alloys. In contrast to thermal
spraying processes, which do not penetrate the substrate material, in the welding technique,
the coating is deposited by melting the coating material onto the substrate and fusing the
molten material to the substrate. Mixing of a proportion of substrate metal with the weld, can
affect the composition and the microstructure and hence the wear resistance. However,
because of the melting of the substrate metal in the fusion zone, on solidification of the weld
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there is metallurgical continuity (or graded interface) across the fusion boundary. Welding
process, however, is preferred for applications requiring dense, relatively thick coating with
high bond strength (14-15).
1.4.1.2 Vapor Deposition
Many soft and hard coatings are deposited by vapor deposition processes and these
techniques are used to produce rather thin coatings (as low as a couple of nanometers thick)
with excellent adhesion (16). Vapor deposition processes reproduce surface topography and
generally do not require postfinishing. However, special equipment is required for vapor
deposition processes. A major disadvantage of the process is high capital cost associated with
vacuum systems. Some important and most popular vapor deposition processes are described
as follows:
Physical Vapor Deposition
Physical vapor deposition (PVD) processes involve the formation of a coating on a substrate
by physically depositing atoms, ions, or molecules of a coating species. PVD is used to apply
coatings by condensation of vapors in high vacuum (10-6-10 Pa). The substrate must be
preheated to ensure coating adhesion and to obtain proper coating structure (4).
Chemical Vapor Deposition
Chemical vapor deposition (CVD) involves the formation of a coating atomistically (atom by
atom) on the hot substrate surface by the reaction of the coating substance with the substrate.
The chemical reactions generally take place in the temperature range of 150-22000C at a
pressure ranging from about 65 Pa to atmospheric pressure (0.1 MPa). The CVD process at
low pressure allows the deposition of coatings with superior quality and uniformly over a
large substrate area. CVD coating usually exhibits superior adhesion compared to those
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deposited by PVD processes, but requirement of high substrate temperature limit their
application to substrates which can withstand high processing temperatures (4).
1.4.1.3 Plating
Plating processes are widely used for application of metallic, nonmetallic and polymer
coatings for wear and corrosion resistance. The adhesion and wear resistance of these
coatings are not as good as those of vapor deposited coatings and coating adhesion is
sometimes not adequate for severe tribological applications. However, they are cheaper
deposition processes. In brief, some important and most popular plating processes are given
below:
Electrochemical deposition
Electrochemical deposition is the most convenient method of applying wear-resistant
coatings of hard metals such as chromium and nickel with high melting points. In this
process, the coating is applied by making the substrate the cathode and the donor material the
anode in an electrolytic bath. An electric potential to the cell results in electrochemical
dissolution of the donor material, which gets coated to the substrate. Coatings can be applied
to any metal surface at room temperature or slightly higher temperature ( < 1000C ) (4).
Atomized Liquid Spray Coatings
Liquid spray processes are most economical and are widely used for paint application and
application of organic and inorganic solid lubricants. All the processes atomize the fluid into
tiny droplets and propel them to the substrate. Atomization of the liquid containing coating
powder particles is accomplished by the use of compressed air (4).
1.4.2 Surface Treatment Techniques
Surface treatment processes are generally used to increase the surface hardness in order to
improve the wear resistance. Some processes also improve fatigue resistance and corrosive
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resistance. Surface treatments are normally applicable to ferrous alloys and mainly divided
into two categories such as microstructural treatments and chemical diffusion treatments. In
brief, the most important and popular surface treatment techniques are described as follows:
1.4.2.1 Microstructural Treatments
In most microstructural treatments, a thin surface shell of ferrous metal (steels and cast irons)
is case-hardened by localized surface heating and quick quenching to produce a hard, wear-
resistant martensitic structure with a tough, ductile core. The fatigue strength is increased
with this process because the treated surface is left with compressive residual stresses (17-18).
The heat-treated parts are used in severe applications requiring wear-resistance even at very
high compressive stresses, such as bearing surfaces, gears, rotating shafts, cams, tappets, and
piston rings. Two surface hardening techniques, induction hardening and flame hardening are
widely used and briefly described as follows:
Induction Hardening
In induction hardening, the medium-carbon steels containing 0.3-0.5% carbon are generally
treated. In this process, a high-frequency alternating current induces eddy currents in the
surface of the steel components which consequently become heated and the surface reaches
the austenitizing temperature. The depth of penetration of the heat is influenced by the power
density and frequency of the alternating current applied in the conductor coil and the time for
which the current is applied. After the heating, the work is rapidly quenched to form hard
martensitic structure. The time required for induction hardening is short (1-30 s), and
components can be heat-treated with practically no scaling. However, the capital cost of
induction hardening is high (4).
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Flame Hardening
Flame hardening is similar to induction hardening in terms of materials processed and their
application. But instead of using an induction current to rapidly heat the surface of a ferrous
base metal, heating is achieved either by direct impingement of a high-temperature flame or
by high-velocity combustion product gases. Flame hardening can be done with minimal
equipment requirements and is particularly useful for components which would be too large
for conventional induction surfaces. However, excessive scaling is formed on the heat-treated
surfaces (4).
1.4.2.2 Chemical Diffusion Treatments
A variety of commercial thermochemical diffusion treatments increases the hardness of
metals, particularly steel and iron parts. At elevated temperatures, chemical species can be
diffused into most iron and steel alloys at significant rates. It is done by exposing heated
ferrous parts to an appropriate medium, which may be a solid, liquid, gas, or plasma. Atom-
by-atom transfer occurs from the medium to the part, thus modifying the surface chemistry
and creating a new alloy at the surface. Surface treatments such as carburizing and nitriding
are the most prominent for tribological applications to achieve the required changes in
surface chemistry and metallurgical structure (19-21). In brief, these treatments are given as
follows:
Carburizing
Carburizing is the process of diffusing carbon into the surface of ferrous metal to increase the
surface carbon content to a sufficient level so that the treated surface will respond to
subsequent quenched hardening. During carburizing, the carbon content of a low-carbon
(0.1-0.2% C) steel surface is increased by heating the steel to about 9250C (so that it is in the
austenitic condition) and holding it in the presence of a carbon-rich medium, which can be a
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solid (charcoal), molten salt, gas, or plasma. These parts are then directly quenched or cooled,
reheated, and again quenched to get the desired martensitic structure. During case hardening,
it is usual to obtain a surface carbon composition of 0.65-0.8%, which produces a high
surface hardness. Carburizing can produce very thick cases with a hardness of up to 850 HV,
which is accompanied by improved wear resistance. However, high-temperature treatment
causes some distortion.
Nitriding
Nitriding treatments are ferritic thermochemical treatments for low-alloy and tool steels, and
they usually involve the introduction of atomic nitrogen into the ferritic phase in the
temperature range of 500-5900C. Nitrogen is introduced into the surface of steel by reaction
with a gas or solid phase or by a nitrogen-containing plasma. Components are cooled slowly
in the furnace under a protective atmosphere and subsequent heat treatment is not needed. It
can make cases that are harder than carburized cases but nitriding is slower than carburizing.
Quenching is not needed and therefore, distortion is minimal. Hard nitriding case has utility
in wear systems.
A variety of coating materials and a variety of coating deposition and surface treatment
techniques are used for tribological applications to combat wear and the most important ones
have already been discussed. The selection of a coating material/deposition or surface
treatment technique for an engineering component is dependent upon functional requirements,
ease of processing and manufacturing cost.
1.5 Review of Applications of Thermally Sprayed Cermet Coating
Thermal spraying is one of the most important material processing or surface modification
technologies and new advances in the technology have extended the applications of thermally
13
sprayed coatings in various fields of industry for enhancing the surface characteristics of a
material or extending its service life (22). Nowadays, thermally sprayed coatings are
commonly employed to enhance the wear resistance of a wide range of engineering
components.
During the last 15-20 years, in the field of thermal spraying, main attention has been paid
to various high velocity spray processes (particle velocity exceeding 300 m/s). The rapid
development of the high velocity oxy-fuel (HVOF) thermal spray method makes possible this
coating technology to satisfy the growing needs of the market for high wear resistance. The
latest HVOF deposition systems are designed to optimize the velocity and temperature of the
spray particles, hence decreasing the level of in-flight chemical reactions and improving the
bonding throughout the coating. The resulting coatings are more durable in wear applications
due to their high hardness, low porosity, reduced quantity of undesirable reaction products
and uniform compressive residual stress when compared to the plasma spraying method (23-
27).
Finally, the coating material plays a dominant role in controlling the tribo-mechanical
properties of the coating. Cermets are widely used in many engineering applications for their
high levels of wear resistance. Among them, the most attractive proved to be tungsten
carbide (WC) based cermets. This is because carbides are very hard and in general, they are
harder than nitrides and tungsten carbide is known to have, beside the high hardness for
which it is firstly chosen, a certain degree of ductility compared with the other carbides.
Moreover, the elastic modulus of tungsten carbide is the highest among refractory ceramics
and significantly higher than other carbides (4). The hard WC particles lead to high coating
hardness while the metal binder (Co, Ni, CoCr or NiCr) supplies the necessary coating
toughness, thus forms not only very hard but also tough cermet system, making it suitable for
14
numerous industrial applications to combat wear. The tungsten carbide cermet powders can
be sprayed using different spray processes such as plasma spraying and HVOF spraying. The
coating properties are influenced not only by the properties of the used powders but also
significantly by the used spray process and spray parameters (28-29). HVOF spraying
process has been widely used for producing high quality carbide cermet coatings due to its
moderate process temperature and significantly high particle velocity. Limited porosity and
minimal microstructural defects with high cohesive strength of HVOF cermet coatings lead
to high fracture toughness. These coating characteristics are advantageous in rolling contact
fatigue performance of machine elements and are explained in a number of published
literatures (30-35).
1.6 Background and Objective of this Study
In recent years, the quality and reliability of thermally sprayed coatings have been improved
remarkably to satisfy the growing needs of the market for high wear resistance of engineering
components. This is due to the development of new processes so that the coating deposition
system can be designed to optimize the velocity and temperature of the spray particles or due
to the introduction of advanced techniques such as application of heat sources with higher
energy and controlling the spray parameters (22,36). Among the cermet coatings, the most
attractive proved to be the hard coatings of tungsten carbide (WC) based cermets because of
its excellent tribological properties such as wear resistance and sliding performance (37), so
that a wide variety of applications to the contact surfaces of machine elements are anticipated.
To date, there are very limited studies concerning the surface durability or the tribological
properties of sprayed coatings in rolling/sliding contact conditions (34-35), although some
15
simple evaluation tests such as the indentation hardness test, scratch test, and wear resistance
test under sliding conditions have been rather extensively carried out.
Recently, durability of thermally sprayed WC cermet coating under rolling/sliding contact
conditions has been the study of much investigation. Using a two-roller testing machine,
Nakajima et al. examined the surface durability of thermally sprayed WC-Cr-Ni cermet
coating in lubricated pure rolling or rolling with sliding contact conditions (38-39). In both
these cases (38-39), cermet coating was formed onto the blasted substrate surface. The coated
roller formed by the conventional type high velocity oxy-fuel flame spraying (HVOF) or by
the high energy type flame spraying (Hi-HVOF) (40) process, was mated with the carburized
steel roller without coating. They found that the flaking of coating is apt to occur when the
coated roller is placed on the slower side in rolling with sliding conditions and the life to
flaking increases as the coating thickness is increased (38). They also clarified that the
spraying conditions and the substrate material have significant effects on the surface
durability of coated roller (39). Based on the results of elastic-plastic analysis of subsurface
layer, they also explained the effects of substrate material, coating thickness and slip ratio on
the durability of coated roller.
Thermal spraying process applies a consumable in the form of a spray of finely divided
molten or semimolten droplets to produce a coating. Any material can be thermally sprayed
as long as it melts or becomes plastic in the heating cycle and if it does not degrade in
heating. Because the deposit does not fuse with the substrate during the spraying operation, it
is possible to ignore metallurgical compatibility. The coating does not have to form a solid
solution with the substrate to achieve a metallurgical bond which is an extremely significant
feature of thermal spraying process (2). In thermal spraying, as the deposit does not fuse with
the substrate to allow coalescence between the coating and the substrate, the bond to the
16
substrate is assisted by roughening the surface. Therefore, in thermal spraying, surface
preparation plays a vital role for good mechanical locking action between the coating and the
substrate. In order to achieve enhanced tribological performance, the coating must remain
firmly attached to the substrate, and for this reason, correct surface preparation prior to
coating is essential to improve the adhesion of coating to the substrate (41).
Much of the tribological research is commercially oriented and modern technology is
continually demanding low friction and high wear-resistant materials in order to improve the
tribological performance of machine elements such as gears, traction drives, cams and
tappets. In recent years, the strongest demand has been for wear-resistant coating materials
particularly tungsten carbide based cermets for enhancing the surface characteristics of a
material or extending its service life under severe tribological and environmental constraints.
Recently, few investigations have been carried out on the durability of WC cermet coating
that is already been discussed. But much more investigations needed to understand clearly
the effects of substrate surface finish on the durability of WC cermet coating because
substrate surface preparation actively plays an important role for the degree of adhesion of
coating to the substrate which in turn may affect significantly the rolling contact fatigue life
of machine elements. In addition, for better understanding of the durability of WC cermet
coating, there is still more investigations needed how substrate material affects the durability
of the coating under extreme operating conditions such as high contact pressure, high speed,
high tangential force, and rough mating surface.
Therefore, taking into consideration all these issues, the main objective of this study was
to investigate the effects of substrate surface finish and substrate material on durability of
WC cermet coating under rolling/sliding contact conditions. Moreover, it was aimed at
investigating the effects of friction, coating thickness, contact pressure, and mating surface
17
roughness on the durability of WC cermet coating. Finally, in order to discuss the durability
of WC cermet coating, theoretical calculations of the elastic-plastic behavior of the
subsurface layer have been carried out using finite element method.
1.7 Structure of the Thesis
In this thesis, chapter 2 describes the testing machine, details of the mating roller specimens,
experimental conditions and procedures that were used throughout this research study.
Chapter 2 also describes the substrate surface finish and thermally sprayed WC cermet
coating.
Chapter 3 presents a review of the pertinent literature of theoretical analysis. The model of
finite element method analysis for analyzing the elastic-plastic behavior of the subsurface
layer under repeated rolling with sliding contact loads is also described in chapter 3.
The results and discussion of this research study are outlined in chapters 4 to 6. These
chapters describe in detail the experimental and theoretical results. Moreover, at the end of
every chapter, there is conclusion of the obtained results.
Finally, conclusions of the obtained results and subjects for future research are given in
chapter 7.
18
Chapter 2
Experimental Procedure
2.1 Introduction
Using a two-roller testing machine, the surface durability of thermally sprayed WC-Cr-Ni
cermet coating was examined in lubricated rolling with sliding contact conditions. Prior to
spraying of the coating, three types of substrate surface finish were prepared by axially
grinding, blasting and circumferentially grinding. The WC cermet coating was formed onto
these axially ground, blasted and circumferentially ground roller specimens made of a
thermally refined carbon steel or an induction hardened carbon steel by means of the high
energy type flame spraying (Hi-HVOF) method. In the experiments, the WC cermet coated
roller was mated with the carburized steel roller without coating in line contact condition.
The details of the mating roller specimens, substrate surface finish, WC cermet coating,
experimental conditions and procedures are given as below.
2.2 Experimental Details
2.2.1 Testing Machine and Test Rollers
Experiments were carried out using a two-roller testing machine having a center distance of
60mm which is shown in Fig. 2.1a. Fig. 2.1b shows the main part of the testing machine. Fig.
2.2 shows the shapes and dimensions of test rollers. Cylindrical specimens F roller without
19
coating and D roller with WC cermet coating were mated. The outside diameter of both
rollers is 60mm and the effective track width is 10mm. In rolling with sliding conditions, a
pair of rollers F/D were forcibly driven by gears with the gear ratios of 27/31 (slip ratio given
for the coated D roller side s=-14.8%) and 25/32 (s =-28.0%).
Fig. 2.1b Main part of the testing machine
Fig. 2.1a Two-roller testing machine
20
The testing machine was equipped with an automatic stopping device which worked in
response to the abnormal vibration induced by the occurrence of flaking or any other surface
damages. The life to flaking or the rolling contact fatigue life N is defined as the total number
of revolutions of the flaked roller side. When the testing machine continued to run without
any serious damage, the running was discontinued at N=2×107 cycles.
The material of F roller was a carburized and hardened chromium molybdenum steel
(SCM415 according to JIS G4105). As the substrate material of D roller, an induction
hardened carbon steel (S45C according to JIS G 4051) and a thermally refined carbon steel
(S45C) were used. Prior to spraying, the substrate surface of D roller was finished to a
roughness of Ry=5.0~8.0µm by axially grinding, blasting, and circumferentially grinding.
The three types of substrate surface finish such as axially ground, blasted and
circumferentially ground are shown in Fig. 2.3.
Fig. 2.2 Test rollers
21
Fig. 2.4 shows the cross-sectional view of the thermally sprayed WC(Bal.)-Cr(20mass%)-
Ni(7mass%) cermet coating. Fig. 2.5a shows SEM observation of WC-Cr-Ni cermet coating.
Fig. 2.5b shows the X-ray observation of WC particles. The white marked areas are carbide
particles. Figs. 2.5c and 2.5d show the X-ray observation where the white marked areas are
Cr and Ni particles respectively.
(a) Axially ground (b) Blasted (c) Circumferentially ground
Fig. 2.3 Substrate surface before coating
Fig. 2.4 Cross-section of sprayed coating
22
As shown in Fig. 2.6, the WC-Cr-Ni cermet coating was formed onto the axially ground,
blasted and circumferentially ground substrate surface of D rollers by the high energy type
flame spraying (Hi-HVOF) method where as a combustion-assisting gas and a fuel gas,
oxygen and kerosene were used at pressures of 1.0 and 0.9MPa, and at flow rates of 53.6 and
0.02m3/h, respectively. The spraying distance was 380mm and the velocities of gas and
cermet particles were 2160 and 1080m/s, respectively. The contact surface of D roller after
(a) WC-Cr-Ni (SEM) (b) WC (X-ray)
(c) Cr (X-ray)
Fig. 2.5 Observation of WC-Cr-Ni cermet coating and its component particles
40µm
23
spraying was finished smooth to a mirror-like condition with a roughness of 0.1~0.2µm Ry
by grinding and subsequent polishing.
2.2.2 Experimental Conditions and Procedures
The Hi-HVOF sprayed D roller and the carburized F roller without coating were mated under
rolling with sliding conditions, and the coated D roller was placed on the slower (driven) side
(slip ratio s=-14.8% or s=-28.0%). Using a coil spring, the normal load was applied in line
contact condition. The rotational speed of the driving side roller was 3580±15rpm. As
lubricant, a paraffinic mineral oil without EP additives (kinematic viscosity ν: 62.9mm2/s at
313K, 8.5mm2/s at 373K, pressure-viscosity coefficient α: 13.3GPa-1 at 313K, specific
gravity 288/277K: 0.878) was supplied to the inlet side of rotating rollers at a flow rate of
15cm3/s and at a constant oil temperature of 318K. The theoretical EHL oil film thickness
hmin was calculated using the oil viscosity at the actual temperature of the roller surfaces
which was measured successively by trailing thermo-couples. For reference, the oil film
thickness for the inlet oil temperature of 318K (450C) was also calculated and is shown in the
Tables (Chapter 4-6). The state of oil film formation between two rollers was continuously
monitored by means of an electric resistance method (42). The friction force between rollers
Fig. 2.6 Cross-sections of sprayed coating (Sections perpendicular to roller axis)
24
was measured using strain gauges stuck on the driving shaft (via slip rings). The main results
such as number of cycles N in each test (whether flaking occurred or not), weight loss due to
flaking and/or wear of each roller, coefficient of friction etc. are shown in Tables (Chapter 4-
6).
25
Chapter 3
Theoretical Analysis
3.1 Introduction
Surfaces that are in rolling or sliding contact almost invariably suffer from some degree of
plastic deformation. Many experiments show that both sliding wear and the initiation of
contact fatigue cracks can be attributed to near surface plastic deformation and eventual
failure of the machine components. Therefore, clear understanding of the plastic deformation
caused by surfaces under rolling with sliding contact is an important phenomenon in rolling
contact fatigue life of machine elements.
3.2 Review of Theoretical Studies
The analysis with the assumption of rolling/sliding contact based on Hertz’s theory, where
the contact width and pressure distribution are assumed to remain Hertzian after the body
begins to deform plastically. With this procedure, Merwin and Johnson attempted to explain
the mechanism of forward flow by an approximate numerical analysis of the elastic-plastic
stress cycles to which the material is subjected in repeated rolling contacts (43). On the basis
of an ideal elastic-perfectly plastic and isotropic material, they showed that a forward
displacement of the surface would be expected as a result of the complex cycle of stress and
strain encountered in rolling contact. Bhargava et al. (44-45) presented finite element
26
analyses of plane strain, elastic-plastic, repeated frictionless rolling contacts. Later, based on
the finite element analysis proposed by Bhargava et al. (44-45), Ham et al. (46) analyzed the
stresses, strains, and deformations produced by repeated, two-dimensional rolling-sliding
contacts. Using the finite element method, Kumar et al. (47) analyzed the plastic deformation
of high strength bearing steel under repeated rolling-sliding contact.
Tribological properties of the surfaces in contact can be improved by coating the surfaces
with hard and wear-resistant layers such as ceramics. Because of the mechanical properties
difference between the ceramic layer and the steel substrate, and in view of the finite
thickness of the layer, accurate solutions for the elastic-plastic deformation cannot be
extracted from the work on homogeneous media. The elastic-plastic contact problem of a
layered half-space indented by a rigid surface was solved by Komvopoulos (48) with the
finite element method. The case of a layer stiffer and harder than the substrate was analyzed
and solution for the contact pressure, subsurface stresses and strains, and location, shape, and
growth of the plastic zone were presented for various layer thickness. Gupta and Walowit
(49) pointed out that for a substrate softer than the coating layer, the pressure substantially
deviate from an elliptical behavior even in an elastic body for the cases of the layer with the
finite thickness. However, it is reasonable to assume that the contact pressure and the contact
width between the cylinder and the coated layer remain approximately Hertzian. Using the
finite element method, Ishikawa et al. (50-51) investigated the deformation of steel substrate
surface coated with a layer of ceramics in rolling-sliding contact. They found that the layer
thickness and the mechanical properties of the substrate significantly affect the deformation,
and the distributions of stress and strain in the substrate. They also found that the sliding or
the friction affects noticeably the deformation of an elastic-plastic material.
27
Therefore, to understand clearly the elastic-plastic behavior of the subsurface layer under
repeated rolling/sliding contact, rolling and sliding were simulated by translating normal and
tangential surface tractions across the surface of an elastic-plastic model and in brief, it is
described in the following section.
3.3 Elastic-Plastic Analysis
In order to discuss the durability of WC-Cr-Ni cermet coating, theoretical analyses of the
elastic-plastic behavior of the subsurface layer under repeated rolling with sliding contact
loads were carried out using finite element method (FEM). The model of finite element
method analysis for analyzing the elastic-plastic behavior of the subsurface layer under
repeated rolling with sliding contact loads is shown in Fig. 3. The rolling/sliding contacts of
the two rollers were simulated by a Hertzian contact stress p(x) and a tangential traction f(x)
moving from the negative to the positive direction along the x-axis on a semi-infinite plate
assumed to be plane strain condition (52-53). p(x) and f(x) are given as follows:
( ) ( ) 2201 bxxPxp H −−= (1)
( ) ( )xpxf ×= µ (2)
where PH is the maximum Hertzian stress, b is the half-width of Hertzian contact, x0 is the x
coordinates of the center of contact load, and µ is the frictional coefficient.
In the finite element method analysis, the process was analyzed in the same way as
Murakami et al. (54) in which the contact load moves from xo = -2b to xo = +2b along the X-
axis. The elastic-plastic behavior in the vicinity on the Y-axis (x0=0) is considered to be
almost equal to the practical situations. In the FEM analysis, the incremental theory for
plastic deformation and the isotropic hardening rule were applied to the plastic deformation
of material and as a criterion for yielding of the elements, von Mises’ yield criterion was
28
used (55-57). The boundary conditions on the sides BC, CD and DE were given as ∆u = ∆v =
0, where ∆u and ∆v are x and y components of the displacement, respectively.
The details of the model for a particular problem and the calculation results such as the
effects of substrate surface finish, substrate material, coating thickness and friction on the
residual stress and plastic strain will be given in detail fashion in chapter 4 to 6.
(a) Whole view of analytic domain
(b) Details of part A
Fig. 3 Model for finite element method (FEM) analysis
29
Chapter 4
Durability of WC Cermet Coating under
Rolling/Sliding Contact
4.1 Introduction
Surface durability of thermally sprayed WC-Cr-Ni cermet coating in lubricated rolling with
sliding contact conditions was examined using a two-roller testing machine. The coating was
formed onto the axially ground, blasted and circumferentially ground roller specimens made
of a thermally refined carbon steel or an induction hardened carbon steel by means of the
high energy type flame spraying (Hi-HVOF) method. The WC cermet coated roller finished
to a mirror-like condition was mated with the carburized steel roller without coating having a
surface roughness of Ry=3.0~5.0µm. In the experiments, a maximum Hertzian stress of
PH=0.6 or 0.8GPa was applied for the thermally refined carbon steel roller and PH=1.4GPa
was applied for the induction hardened carbon steel roller in line contact condition. As a
result, it was found that in the case of induction hardened steel substrate, the coated roller
generally exhibits a long life without any serious damage and the surface durability is hardly
affected by the substrate surface finish, while in the case of thermally refined steel substrate,
the durability of coated roller is lowered and the life to flaking is very short particularly when
the substrate surface is circumferentially ground and the mating surface is rough. The surface
durability of coated roller was also compared with the durability of steel roller without
30
coating. Moreover, in order to discuss the durability of coated steel roller, theoretical
calculations were carried out on the elastic-plastic behavior of the subsurface layer under
repeated rolling with sliding contact loads using a finite element method (FEM). The
experimental results and discussion and the theoretical analyses are given in the following
sections.
4.2 Experimental Details
Experiments were carried out using a two-roller testing machine and the materials, shapes
and dimensions of the test rollers are described in chapter 2. Table 4.1 shows a summary of
experimental results. The surface hardness of F roller was HV=749~853. The contact surface
of F roller was roughened to a surface roughness of Ry=3.0~5.0µm (Ry: maximum height of
the profile according to ISO 4287-1997 or JIS B 0601-1994, sampling length 0.25mm) by
cylindrical grinding. The hardness of D roller for thermally refined steel substrate was
HV=304~332 and for an induction hardened steel substrate was HV=669~733. The details of
the substrate surface finish and the WC-Cr-Ni cermet coating are described in chapter 2. The
coatings of about 60µm and 110µm in thickness were prepared. The micro-Vickers hardness
of the coating formed by Hi-HVOF was HV=1001~1151 (test load: 2.94N).
In tests AA and BA, axially ground substrate rollers, in tests AB and BB, blasted
substrate rollers and in tests AC and BC, circumferentially ground substrate rollers were used.
Moreover, in test CC-1, cylindrical ground carburized steel D roller without coating was
mated with the F roller without coating (steel on steel test). A maximum Hertzian stress of
PH=0.6 or 0.8GPa was applied for the thermally refined carbon steel roller and PH=1.4GPa
was applied for the induction hardened carbon steel or carburized hardened steel roller. The
main results such as number of cycles N in each test (whether flaking occurred or not),
31
weight loss due to flaking and/or wear of each roller, coefficient of friction etc. are shown in
Table 4.1.
Roughness Ryd, µm
Test No.
Hardness
HVb
Thicknessc, µm
Before After
Hertz stress PH
e, GPa
Slip ratio s,%
Coefficient of friction
, µ
hmin
f, µm
(318K)
Number of cycles N, x 104
Weight loss, g
Surface damage
AA-1 F Da
777 1113/ 328
56 4.0 0.2
3.0 1.0
0.6 -14.8 0.055
~ 0.036 0.63
(1.33) 2000
0.01 0.00
F: No D: No
AA-2 F Da
759 1111/ 327
52 4.0 0.2
2.0 1.0
0.8 -14.8 0.062
~ 0.037 0.56
(1.24) 2000
0.01 0.00
F: No D: No
AB-1 F Da
786 1090/ 330
54 4.0 0.2
6.0 3.0
0.8 -14.8 0.067
~ 0.035 0.54
(1.24) 1197
0.07 0.08
F: No D: Flaking
AB-2 F Da
789 1115/ 330
106 4.0 0.1
3.0 1.0
0.8 -14.8 0.065
~ 0.034 0.63
(1.24) 2000
0.02 0.01
F: No D: No
AC-1 F Da
779 1151/ 318
67 5.0 0.1
8.0 2.0
0.6 -14.8 0.057
~ 0.034 0.53
(1.33) 342
0.08 0.11
F: No D: Flaking
AC-2 F Da
789 1124/ 304
63 5.0 0.1
10.0 3.0
0.8 -14.8 0.065
~ 0.038 0.54
(1.24) 25
0.13 0.23
F: No D: Flaking
AC-3 F Da
853 1128/ 332
107 4.0 0.1
2.0 1.0
0.8 -14.8 0.063
~ 0.035 0.74
(1.24) 2000
0.01 0.01
F: No D: No
BA-1 F Da
816 1131/ 684
61 3.0 0.1
2.0 1.0
1.4 -28. 0 0.050
~ 0.032 0.18
(1.03) 2000
0.02 0.02
F: No D: No
BA-2 F Da
774 1080/ 703
67 5.0 0.1
3.0 1.5
1.4 -28.0 0.049
~ 0.036 0.13
(1.03) 2000
0.02 0.01
F: No D: No
BB-1 F Da
749 1140/ 733
52 3.0 0.2
2.0 3.0
1.4 -28.0 0.042
~ 0.031 0.18
(1.03) 2000
0.01 0.01
F: No D: No
BB-2 F Da
818 1027/ 678
55 5.0 0.1
3.0 2.0
1.4 -28.0 0.054
~ 0.036 0.14
(1.03) 2000
0.01 0.01
F: No D: No
BC-1 F Da
803 1115/ 704
52 3.0 0.2
2.0 2.0
1.4 -28.0 0.054
~ 0.047 0.13
(1.03) 2000
0.02 0.03
F: No D: No
BC-2 F Da
788 1137/ 692
50 4.0 0.1
3.0 3.0
1.4 -28.0 0.056
~ 0.035 0.17
(1.03) 2000
0.04 0.01
F: No D: No
BC-3 F Da
807 1001/ 669
58 5.0 0.1
2.0 2.0
1.4 -28.0 0.051
~ 0.039 0.16
(1.03) 2000
0.09 0.09
F: No D: Flaking
BC-4 F Da
817 1132/ 714
113 5.0 0.1
3.0 2.0
1.4 -28.0 0.051
~ 0.038 0.16
(1.03) 2000
0.02 0.02
F: No D: No
CC-1 F D
797 - / 791
- 4.0 0.2
3.0 6.0
1.4 -28.0 0.076
~ 0.043 0.16
(1.03) 452
0.04 0.20
F: Pitting D: Pitting
aWC/CrNi cermet coated roller by Hi-HVOF. bSurface hardness of F roller and coating hardness / substrate hardness of coated D roller. cThickness of coating. dRy: maximum height of the profile according to ISO 4287-1997 and JIS B 0601-1994 (sampling length 0.25mm). ePH: maximum Hertzian stress. fhmin: EHL minimum oil film thickness calculated using the oil viscosity at roller surface temperature. ( ) is hmin for the inlet oil temperature 45oC (318K).
Table 4.1 Summary of experiments and main results
32
4.3 Results and Discussion
4.3.1 Comparison of Surface Durability
Fig. 4.1a shows the effect of substrate surface finish on surface durability or life to flaking of
WC cermet coated steel roller with the coating thickness of about 60µm. In the case of
thermally refined steel substrate, the life to flaking was remarkably affected by the substrate
surface finish. Namely, in the case of axially ground substrate, life to flaking was prolonged
up to N=2×107 cycles without any surface damage. On the other hand, in the case of blasted
and circumferentially ground substrate, flaking occurred on the coated roller. Especially, the
circumferentially ground substrate roller showed a very short life. Furthermore, as shown in
Table 4.1, the life to flaking was remarkably improved with the increase in the coating
thickness from 60µm to 110µm.
Fig. 4.1a Effects of substrate surface finish and substrate material on life to flaking (Thickness≈60µm)
1.0E+04
5.0E+06
1.0E+07
1.5E+07
2.0E+07
Nu
mb
er o
f cyc
les N=2.0 x 107
N=2.0 x 107
N=2.0 x 107
N=1.2 x 107
N=2.0 x 107
N=2.5 x 105
Axially ground
Circumferentially groundBlasted
Induction hardened steel, PH=1.4GPa,s=-28.0%,RyF≈4.0µm
Thermally refined steel, PH=0.8GPa,s=-14.8%,RyF≈4.0µm
33
In the case of induction hardened steel substrate, the life to flaking was not influenced by
the substrate surface finish, and it was possible to run up to N=2×107 cycles in spite of severe
running conditions of Hertz stress PH=1.4GPa and slip ratio s=-28.0%. Besides these results,
the relation between the life to flaking and the mating surface roughness is illustrated in Fig.
4.1b, and it is shown that it was possible to run up to N=2×107 cycles even when the mating
F roller surface was roughened to RyF=5.0µm. However, as shown in Table 4.1, there was a
little difference in occurrence of flaking depending on the substrate surface finish. Namely,
in the case of axially ground and blasted substrate, no flaking occurred even when the mating
surface roughness was RyF=5.0µm. On the other hand, in the case of circumferentially
ground substrate, a small amount of flaking occurred before N=107 cycles when the mating
surface roughness was RyF=5.0µm. Moreover, it was also shown that the occurrence of
flaking is restrained due to the increase in the coating thickness.
Fig. 4.1b Effect of mating surface roughness on life to flaking (Induction hardened steel: Thickness≈60µm, PH=1.4GPa, s=-28.0%)
1.0E+04
5.0E+06
1.0E+07
1.5E+07
2.0E+07
Nu
mb
er o
f cyc
les N=2.0 x 107
N=2.0 x 107N=2.0 x 107
N=2.0 x 107
N=2.0 x 107
N=2.0 x 107
Axially ground
Circumferentially groundBlasted
RyF=5.0µm
RyF=3.0µm
34
From Table 4.1 it can be seen that in test CC-1 (steel on steel test), where a carburized
steel D roller without coating was mated with the carburized steel F roller, many pits
occurred on not only D roller surface but also F roller surface and the fatigue life of the non-
coated roller was fairly shorter compared with that of the coated roller in test BC-2.
4.3.2 Changes in Surface Profile
Fig. 4.2 shows the profile curves of the mating surfaces before and after the tests BC-2 and
CC-1. In test BC-2 where the coated D roller was used in the follower side, after running, the
Before running
After running
5 µ
m
0.5 mm
Fig. 4.2 Profile curves of mating surfaces before and after running (PH=1.4GPa, s=-28.0%, RyF= 4.0µm)
Before running
After running
F
D
F
D
BC-2
CC-1
F
D
D
F
F D
35
surface roughness of F roller and coated D roller became about Ry=3.0 and 3.0µm
respectively. On the other hand, in test CC-1 where a steel D roller without coating was used
in the follower side, the surface roughness of F roller and D roller became about Ry=3.0 and
6.0µm respectively. From the figure it is apparent that the surface profile of D roller changed
remarkably in test CC-1.
4.3.3 States of Oil Film Formation and Friction
Some results of the measurement of the state of oil film formation between rollers are shown
in Fig. 4.3. For fully developed oil film, the voltage Eab recorded on a chart shows 15mV. As
shown in this figure, it is apparent that immediately after the start of running, the voltage was
very near to zero or a very low value due to the severe asperity contacts, then the voltage rose
gradually as the number of cycles increased. In this figure, it is also clear that the processes
of oil film formation were different depending on the running conditions and the mating
surface roughness. Owing to the rapid decrease in the mating surface roughness and the
formation of oxide film under severe operating conditions, the voltage in tests BA-1 and BC-
3 showed a higher value compared with tests AA-2 and AC-2. However, it could be
considered that the state of oil film formation is hardly influenced by the substrate surface
finish and the substrate material.
Fig. 4.4 shows the views of the contacting surfaces before and after the test AA-2 for the
Hertzian stress of PH=0.8GPa and slip ratio s=-14.8%. From the figure, it is clear that after
running, micropits occurred on the coated D roller surface. From Table 4.1, it can also be
seen that after the test, the surface roughness of F roller and D roller became Ry=2.0 and
1.0µm respectively. Fig. 4.5 shows the views of the contacting surfaces before and after the
36
2x107
Number of cycles, N
Vol
tage
Eab
, mV
Circum-ferentiallyRyF=5µm(Test BC-3)
AxiallyRyF=3µm(Test BA-1)
Circum-ferentiallyRyF=5µm(Test AC-2)
AxiallyRyF=4µm(Test AA-2)
104 105 106 107
0
5
10
15
Fig. 4.3 Effects of substrate surface finish and substrate material on states of oil film formation between rollers (Eab=0mV:contact, 15mV:separation, Thickness≈60µm)
Fig. 4.4 Views of contacting surfaces (Test AA-2: PH=0.8GPa, s=-14.8%)
F roller D roller
F roller D roller
Before running
After running
0.1mm
37
test BC-3. Due to the severe running conditions of Hertzian stress PH=1.4GPa and slip ratio
s=-28.0%, oxide film was formed. From the figure it is apparent that because of oxide film
formation, after the test, the color of the coated D roller surface was much changed.
Moreover, from Table 4.1, it can be seen that after the test, the surface roughness of F roller
and D roller became Ry=2.0 and 2.0µm respectively.
Fig. 4.6 shows the comparison of the oil film formation in the cases of with and without
WC cermet coating. In test CC-1 where pitting occurred and the testing machine stopped at
N=4.5×106 cycles, the oil film formation was hardly observed up to N=3.5×105 cycles. On
the other hand, in test BC-2 with coating, oil film came to be built up steadily, and neither
flaking nor pitting occurred up to N=2×107 cycles.
F roller D roller
F roller D roller
Fig. 4.5 Views of contacting surfaces (Test BC-3: PH=1.4GPa, s=-28.0%)
Before running
After running
0.1mm
38
The results of friction measurement in each test are given in Table 4.1 as the coefficient of
friction (initial value ~ steady value) and at the initial stage of running, some of these results
are shown in Fig. 4.7. These results had an almost same tendency as that of oil film formation.
Namely, although obvious differences in the variation of frictional coefficient were observed
depending on the running conditions and the mating surface roughness, it was confirmed that
the substrate surface finish and the substrate material has hardly effect on the friction
coefficient. Fig. 4.8 shows the comparison of friction measurement in the cases of with
and without WC cermet coating. In test BC-2 where the coated D roller was used, the
changes in friction followed almost the same trend but the value of friction coefficient
was lowered compared with test CC-1.
2x107
Vol
tage
Eab
, mV
Number of cycles, N
CoatingRyF=4µm(Test BC-2)
WithoutcoatingRyF=4µm(Test CC-1)
104 105 106 107
0
5
10
15
Fig. 4.6 States of oil film formation between rollers: Comparison of with and without WC cermet coating (Eab=0mV:contact, 15mV:separation, Thickness≈60µm)
39
Coe
ffic
ien
t of
fri
ctio
n µ
Number of cycles N [ x 104 ]
Circum-ferentiallyRyF=5µm(Test BC-3)
AxiallyRyF=3µm(Test BA-1)
Circum-ferentiallyRyF=5µm(Test AC-2)
AxiallyRyF=4µm(Test AA-2)
0 1 2 3 4 5 60
0.02
0.04
0.06
0.08
Fig. 4.7 Effect of substrate surface finish and substrate material on changes in coefficient of friction at the initial stage of running (Thickness≈60µm)
Coe
ffic
ien
t of f
rict
ion
µ
Number of cycles N [ x 104 ]
CoatingRyF=4µm(Test BC-2)
WithoutcoatingRyF=4µm(Test CC-1)
0 1 2 3 4 5 60
0.02
0.04
0.06
0.08
Fig. 4.8 Changes in coefficient of friction at the initial stage of running: Comparison of with and without WC cermet coating (Thickness≈60µm)
40
4.4 Elastic-Plastic Analysis
Taking into consideration the results obtained from the experimental investigation where it
was found that durability or the life to flaking of coated roller was significantly affected by
the substrate surface finish and the substrate material, elastic-plastic behavior of the
subsurface layer under repeated rolling with sliding contact loads was analyzed using a finite
element method (FEM). The analytical model used for the present FEM analysis has been
described in chapter 3. The models of substrate surface finish used for the theoretical
calculations are shown in Figs. 4.9a and 4.9b. According to the roughness variation in the
rolling direction, the circumferentially ground substrate surface was regarded as the smooth
surface, while the axially ground substrate surface and the blasted substrate surface were
regarded as the rough surface as shown in the figures below.
Fig. 4.9b Rough substrate surface
Fig. 4.9a Smooth substrate surface
41
In the FEM analysis, the plane strain quadrangular element with eight nodal points and the
incremental theory for plastic deformation were used. Moreover, the isotropic hardening rule
was applied to the plastic deformation of the material. As a criterion for yielding of the
elements, the von Mises’ yield criterion was used. The boundary conditions were adopted in
the same way as the previous investigation by Nakajima et al. (38-39). The dimensions of the
finite element model are as follows:
The analytic space: 140b х 60b (width х depth)
The number of elements: 1200
The number of nodal points: 3761
The smallest element: 0.2b х 0.05b (width х depth)
The same way as the previous investigation by Ishikawa et al. (50-51), calculations were
performed under the maximum Hertzian stress PH=1.2GPa and the coating thickness was
fixed at 0.15b and 1.5b which are equal to 48µm and 477µm, respectively. Table 4.2 shows
the material parameters used in the numerical calculations. In order to emphasize the effect
of the frictional force on the life to flaking of coated roller, the results for the frictional
coefficient µ=-0.1 are shown in the present figures. Where, the sign of µ defined as negative
when the directions of friction force and load movement are opposed to each other.
Table 4.2 Material parameters
S45C Material
WC- CrNi Thermally
refined Induction hardened
Young’s modulus E, GPa 432 206 206 Poisson’s ratio ν 0.3 0.3 0.3 Yield stress σY , MPa 2060 490 1030 Shear yield stress k, MPa 1189 283 595 Tangent modulus H’, GPa 206 20.6 103
42
Figs. 4.10a and 4.10b show some calculation results of the distributions of residual stress
σx and equivalent plastic strain εpav both in the coated layer and in the substrate layer in the
case of thermally refined steel substrate. In the numerical calculations, since both the residual
stress and the equivalent plastic strain hardly varied after 3 times pass of loading, the
calculation in each condition was discontinued at 3 times pass.
-0.4 -0.2 0 0.2 0.4
0
2
4
6
8
σX/PH
Dep
th/b
PH=1.2GPaµ=-0.13PassThickness=0.15bThermally refined steel
:Smooth substrate:Rough substrate
Thickness=1.5b:Smooth substrate:Rough substrate
Coating(0.15b)
Coating(1.5b)
0 0.001 0.002 0.003
0
2
4
6
8
y/b
εpav
PH=1.2GPaµ=-0.13PassThickness=0.15bThermally refined steel
:Smooth substrate:Rough substrate
Thickness=1.5b:Smooth substrate:Rough substrate
Coating(1.5b)
Coating(0.15b)
Fig. 4.10b Effects of smooth substrate surface and rough substrate surface on plastic strain
Fig. 4.10a Effects of smooth substrate surface and rough substrate surface on residual stress
43
The distribution of the residual stress σx showed a peculiar mode along the Y-axis and it
was tensile in the coated layer whereas below the coated layer, there was an abrupt change in
σx as the coating thickness decreased. It was found that as the coating thickness becomes
thick, the effect of substrate surface finish becomes small and the sudden change in σx near
the coated layer decreases. The distribution of equivalent plastic strain εpav shows that below
the coated layer, the plastic strain increases greatly as the coating thickness decreases. It was
also found that immediately beneath the coating, the plastic strain extremely increased in the
case of smooth substrate surface rather than rough substrate surface. On the other hand, the
plastic strain remained almost zero in the coated layer. The numerical results suggest that
rough substrate surface performs better than smooth substrate surface to improve the
durability of the coated layer when the coating thickness decreases.
Figs. 4.11a and 4.11b show the results of residual stress and equivalent plastic strain both
in the coated layer of WC-Cr-Ni cermet and in the substrate of an induction hardened steel or
a thermally refined steel. Calculations were performed using a rough substrate model under a
maximum Hertzian stress of PH=1.4GPa and the coating thickness was fixed at 0.15b
corresponds to 56µm. It was found that the residual stress σx and the plastic strain εpav vary
significantly in the thermally refined steel substrate whereas the residual stress hardly
changed in the subsurface layer and the equivalent plastic strain remained almost zero in the
case of the induction hardened steel substrate. Consequently, it can be concluded that the
higher hardness substrate is effective to improve the durability of WC cermet coating.
44
-0.4 -0.2 0 0.2 0.4
0
2
4
6
8
σX/PH
y/b
PH=1.4GPa, µ=-0.13PassThickness=0.15b
:Thermally refined
:Induction hardened
Coating(0.15b)
0 0.002 0.004 0.006
0
2
4
6
8
y/b
εpav
PH=1.4GPa, µ=-0.13PassThickness=0.15b
:Induction hardened:Thermally refined
Coating(0.15b)
Fig. 4.11b Effect of substrate material on plastic strain
Fig. 4.11a Effect of substrate material on residual stress
45
4.5 Conclusion
Durability of thermally sprayed WC-Cr-Ni cermet coating in lubricated rolling with sliding
contact conditions was investigated using a two-roller testing machine. The WC cermet
coated steel roller was mated with the carburized steel roller without coating having a surface
roughness of Ry=3.0~5.0µm. Durability of the steel roller without coating was also examined
and compared with that of the coated steel roller. Moreover, FEM analysis on the elastic-
plastic behavior of the subsurface layer under repeated rolling with sliding contact was
carried out. The results are summarized and the following conclusions are drawn:
• In the case of thermally refined steel substrate, the occurrence of flaking was remarkably
restrained when the substrate was axially ground, while the durability of coated roller was
lowered with blasted or circumferentially ground substrate. The life to flaking of WC
cermet coated roller had a tendency to be prolonged as the coating thickness increased,
especially the effect appeared more distinctly with the circumferentially ground substrate
roller.
• In the case of induction hardened steel substrate, the coated rollers exhibited a longer life
compared with the thermally refined steel substrate, and the durability or the life to
flaking showed a little sensitivity to the substrate surface finish. Therefore, the higher
hardness substrate is effective to increase the surface durability of thermally sprayed WC
cermet coating. It was also confirmed that durability of coated steel roller is much higher
than that of steel roller without coating.
• Elastic-plastic analysis of the subsurface layer revealed that rough substrate surface
performs better than smooth substrate surface to improve the durability of coated roller,
46
especially when the coating thickness becomes thin in the lower hardness substrate such
as thermally refined steel.
47
Chapter 5
Effect of Substrate Surface Finish on Durability of
WC Cermet Coating
5.1 Introduction
The surface durability of thermally sprayed WC-Cr-Ni cermet coating in lubricated
rolling/sliding contact conditions was investigated using a two-roller testing machine. The
coating of 60 to 210µm in thickness was formed onto the axially ground, blasted, and
circumferentially ground roller specimens made of a thermally refined carbon steel or an
induction hardened carbon steel by the high energy type flame spraying (Hi-HVOF). The
coated roller finished to a mirror-like condition was mated with the smooth carburized steel
roller without coating having a surface roughness of Ry=0.1~0.4µm, and a maximum
Hertzian stress of PH=1.0 to 1.4GPa was applied in line contact. In the thermally refined steel
substrate roller, the coating on the circumferentially ground substrate generally showed a
lower durability compared with that on the axially ground substrate or blasted substrate, and
this difference appeared more distinctly as the coating thickness decreased. On the other hand,
the induction hardened steel substrate roller showed a higher durability, and the effect of
substrate surface finish was hardly recognized. The effect of substrate surface finish on the
durability of thermally sprayed coating was also examined by the elastic-plastic analysis of
48
the subsurface layer. The experimental results and discussion and the theoretical analyses are
given in the following sections.
5.2 Experimental Details
Experiments were carried out using a two-roller testing machine and the materials, shapes
and dimensions of the test rollers are described in chapter 2. Table 5.1 shows a summary of
experimental results. The surface hardness of F roller was HV=720~783. The contact surface
of F roller was finished smooth to a surface roughness of Ry=0.1~0.4µm (Ry: maximum
height of the profile according to ISO 4287-1997 or JIS B 0601-1994, sampling length
0.25mm) by cylindrical grinding and subsequent polishing. The hardness of D roller for
thermally refined steel substrate was HV=313~337 and for an induction hardened steel
substrate was HV=689~700. The details of the substrate surface finish and the WC-Cr-Ni
cermet coating are described in chapter 2. The coatings of about 60µm, 110µm and 210µm in
thickness were prepared. The micro-Vickers hardness of the coating formed by Hi-HVOF
was HV=1025~1167 (test load: 2.94 N).
In tests AA and BA, axially ground substrate rollers, in tests AB and BB, blasted
substrate rollers and in tests AC and BC, circumferentially ground substrate rollers were used.
A maximum Hertzian stress of PH=1.0 to 1.4GPa was applied in line contact condition. The
main results such as number of cycles N in each test (whether flaking occurred or not),
weight loss due to flaking and/or wear of each roller, coefficient of friction, EHL minimum
oil film thickness hmin etc. are shown in Table 5.1.
49
Table 5.1 Summary of experiments and main results Roughness
Ryd, µm Test No.
Hardness HVb
Thick-ness c, µm Before After
Hertze stress PH, GPa
Slip ratio s, %
Coeffi. of friction, Μ
hminf,
µm (318K)
Number of cycles
N, × 104
Weight loss, g
Surface damage
AA-1 F Da
756 1167 / 337
56 0.2 0.1
0.2 0.1
1.0 -14.8 0.030
~0.023 0.65
(1.17) 2000
0.00 0.00
F:No D:No
AA-2 F Da
750 1127 / 325
114 0.2 0.2
0.2 0.2
1.2 -14.8 0.030
~0.027 0.43
(1.11) 2000
0.00 0.00
F:No D:No
AA-3 F Da
737 1025 / 328
218 0.2 0.1
0.4 0.4
1.4 -14.8 0.029
~0.023 0.27
(1.07) 31
0.07 2.06
F:No D:Flaking
AB-1 F Da
766 1069 / 316
55 0.1 0.1
0.1 0.1
1.0 -14.8 0.031
~0.023 0.61
(1.17) 2000
0.00 0.00
F:No D:No
AB-2 F Da
763 1083 / 332
109 0.1 0.2
0.2 0.2
1.2 -14.8 0.028
~0.022 0.40
(1.11) 161
0.00 1.11
F:No D:Flaking
AB-3 F Da
740 1108 / 278
201 0.1 0.2
0.2 0.1
1.2 -14.8 0.031
~0.026 0.48
(1.11) 2000
0.00 0.01
F:No D:No
AB-4 F Da
728 1140 / 321
207 0.2 0.2
0.4 0.2
1.4 -14.8 0.028
~0.024 0.26
(1.07) 11
0.00 0.15
F:No D:Flaking
AC-1 F Da
772 1082 / 324
60 0.2 0.2
2.0 0.4
1.0 -14.8 0.029
~0.025 0.63
(1.17) 1005
0.03 0.06
F:No D:Flaking
AC-2 F Da
783 1104 / 313
110 0.4 0.2
0.4 0.4
1.2 -14.8 0.030
~0.024 0.38
(1.11) 11
0.02 0.07
F:No D:Flaking
AC-3 F Da
744 1089 / 326
213 0.2 0.2
0.2 0.2
1.2 -14.8 0.029
~0.023 0.50
(1.11) 2000
0.00 0.00
F:No D:No
AC-4 F Da
720 1066 / 332
210 0.4 0.2
1.0 3.0
1.4 -14.8 0.028
~0.022 0.27
(1.07) 64
0.00 3.47
F:No D:Flaking
BA-1 F Da
755 1155 / 689
64 0.1 0.1
0.2 0.4
1.4 -28.0 0.028
~0.022 0.21
(1.03) 2000
0.01 0.01
F:No D:No
BB-1 F Da
783 1104 / 693
64 0.4 0.2
0.4 0.2
1.4 -28.0 0.026
~0.022 0.23
(1.03) 2000
0.00 0.00
F:No D:No
BC-1 F Da
762 1090 / 700
57 0.1 0.2
0.1 0.2
1.4 -28.0 0.025
~0.021 0.22
(1.03) 2000
0.00 0.00
F:No D:No
aWC/CrNi cermet coated roller by Hi-HVOF. bSurface hardness of F roller and coating hardness/substrate hardness of coated D roller. cThickness of coating. dRy:maximum height of the profile according to ISO 4287-1997 or JIS B 0601-1994 (sampling length 0.25mm). ePH: maximum Hertzian stress. fhmin: EHL oil film thickness calculated using the oil viscosity at roller surface temperature.
( ) is hmin calculated for the inlet oil temperature 318K
5.3 Results and Discussion
5.3.1 Comparison of Surface Durability
Fig. 5.1 shows the effect of substrate surface finish on surface durability or life to flaking of
WC cermet coated steel roller in the case of thermally refined steel substrate. With the
50
coating thickness of about 60µm, Hertzian stress of PH=1.0GPa and slip ratio s=-14.8%, the
coated roller exhibited a long life up to N=2×107 cycles in the case of axially ground
substrate (test AA-1) and blasted substrate (test AB-1) whereas circumferentially ground
substrate roller (test AC-1) showed a short life and flaking occurred at nearly N=1.0×107
cycles. With the coating thickness of about 110µm and Hertzian stress of PH=1.2GPa, the life
to flaking was significantly affected by the substrate surface finish. Namely, in test AA-2, the
axially ground substrate roller showed a long life and it was possible to run up to N=2×107
cycles without any surface damage. On the other hand, life to flaking was very short in the
case of blasted and circumferentially ground substrate and particularly, in test AC-2, where
flaking of coating occurred at N=1.1×105 cycles in the case of circumferentially ground
substrate. Moreover, as shown in Table 5.1, flaking of coating was restrained and life to
flaking was remarkably improved with the increase in the coating thickness from 110µm to
210µm.
AxiallyBlasted
Circum-
1.0GPa
1.2GPa
N=2.0×107
N=2.0×107
N=1.0×107N=2.0×107
N=1.6×106
N=11×104
1.0E+04
5.0E+06
1.0E+07
1.5E+07
2.0E+07
Nu
mb
er o
f cy
cles
PH
s=-14.8%
ground
ferentially ground
(110µm)
(60µm)
Fig. 5.1 Effect of substrate surface finish on life to flaking (Thermally refined steel substrate)
51
Fig. 5.2 illustrates the effect of substrate material on life to flaking. With the Hertzian
stress of 1.4GPa and coating thickness of about 210µm, the thermally refined steel substrate
rollers exhibited a very short life. Flaking of coating occurred before N=6.4×105 cycles in the
case of axially ground, blasted and circumferentially ground substrate rollers in tests AA-3,
AB-4, and AC-4. On the other hand, the induction hardened steel substrate rollers exhibited a
fairly high durability up to N=2×107 cycles without any surface distress and the effect of
substrate surface finish on the durability of cermet coating was hardly recognized.
Fig. 5.3 and Fig. 5.4 show a few appearances of the flaking that occurred on the coated D
roller surfaces. In test AB-2 where blasted substrate roller was used, flaking occurred at
N=161×104 cycles and in this case, flaking of coating occurred almost allover the contact
AxiallyBlasted
Circum-
Induction
Thermally
N=2.0×107
N=2.0×107
N=2.0×107
N=31×104
N=11×104
N=64×104
1.0E+04
5.0E+06
1.0E+07
1.5E+07
2.0E+07
Nu
mb
er o
f cy
cles
PH=1.4GPa
ground
ferentially ground
refined(s=-14.8%)
hardened(s=-28.0%)
Fig. 5.2 Effect of substrate material on life to flaking
52
area. In test AC-2 where circumferentially ground substrate roller was used, flaking occurred
at early stage of running N=11×104 cycles and the sectional view of the flaked part is shown
in Fig. 5.4. Fig. 5.5 shows the results of depth of flaking. From these results, it is clear that
for the circumferentially ground substrate roller, flaking of coating developed deep beyond
the interface whereas for the blasted substrate roller, depth of flaking was nearly equal to the
coating thickness and flaking occurred along the interface between the coating layer and the
substrate.
Fig. 5.3 External views of flaked surfaces
Fig. 5.4 Sectional view of flaked part (AC-2 D, Circumferential direction)
53
5.3.2 States of Oil Film Formation
Fig. 5.6 shows some results of the measurement of the state of oil film formation between
rollers. For fully developed oil film, the voltage Eab recorded on a chart shows 15mV.
Results of the states of oil film formation in tests AA-1, AB-1, and AC-1 show that after the
start of running, the oil film between the rollers started to develop quickly because of the
smooth mating surface. It is apparent from the figure that fully developed oil film came to be
built up at nearly N=105~106 cycles. Moreover, it could be considered that state of oil film
formation is hardly affected by the substrate surface finish.
Exp.AC-1PH=1.0GPa
N=1005×104Exp.AC-2
PH=1.2GPa
N=11×104Exp.AB-2
PH=1.2GPa
N=161×104
0
100
200
300
400
500
600
Circum-ferentially
ground
Circum-ferentially
ground
Blasted
Dep
th o
f fl
akin
g,
µm
Coatingthickness
Fig. 5.5 Depth of flaking (Thermally refined steel, s=-14.8%)
54
5.4 Elastic-Plastic Analysis
Taking into consideration the results obtained from the experimental investigation,
theoretical analyses of the elastic-plastic behavior of the subsurface layer under repeated
rolling with sliding contact loads were carried out using a finite element method (FEM). In
view of the fact that in the case of thermally refined steel substrate, the life to flaking of the
coated roller was significantly affected by the substrate surface finish, theoretical calculations
were carried out using the circumferentially ground model and axially ground model and
these models are shown in Figs. 5.7a and 5.7b. The analytic domain used for the FEM
analysis has been described in chapter 3.
104 105 106 107
0
5
10
15
Number of cycles N
Vo
ltag
e E
ab, m
V
2×107
Thermally refined steelPH=1.0GPa, s=-14.8%
:Axially ground:Blasted:Circumferentially
ground
Fig. 5.6 Oil film formation between rollers (Eab=0mV: Contact, 15mV: Separation)
55
In the FEM analysis, the plane strain quadrangular element with eight nodal points and the
plane strain triangular element with six nodal points were used. The incremental theory for
plastic deformation and the isotropic hardening rule was applied to the plastic deformation of
the material. As a criterion for yielding of the elements, the von Mises’ yield criterion was
used. The boundary conditions were adopted in the same way as the previous investigation
by Nakajima et al. (38-39). The dimensions of the finite element model are as follows:
The analytic space: 140b х 60b (width х depth)
The number of elements: 3100 (circumferentially ground model)
The number of nodal points:9563 (circumferentially ground model)
Fig. 5.7a Circumferentially ground model
Fig. 5.7b Axially ground model
56
The number of elements: 3200 (axially ground model)
The number of nodal points: 9663 (axially ground model)
The smallest element: 0.1b х 0.05b (width х depth)
The same way as the previous investigation by Ishikawa et al. (50-51), calculations were
performed under the maximum Hertzian stress of PH=1.2GPa and the coating thickness was
fixed at 0.35b and 0.65b which corresponds to 111µm and 207µm, respectively.
Calculations were carried out for the frictional coefficient µ=-0.03. Where, the sign of µ
defined as negative when the directions of friction force and load movement are opposed to
each other. Table 5.2 shows the material parameters used in the numerical calculations.
Table 5.2 Material parameters
Material Coating Substrate Young’s modulus E, GPa 432 206 Poisson’s ratio ν 0.3 0.3 Yield stress σY, MPa 2060 490 Shear yield stress k, MPa 1189 283 Tangent modulus H’, GPa 206 20.6
Figs. 5.8 and 5.9 show the calculation results of the distribution of residual stress σx both
in the coated layer and in the substrate layer. In the numerical calculations, since the residual
stress hardly varied after 5 times pass of loading, the calculation was discontinued at 5 times
pass and the calculation results are shown up to 5 pass of loading. Calculations were carried
out for Hertzian stress of PH=1.2GPa and frictional coefficient µ=-0.03. Fig. 5.8 shows the
effect of coating thickness on residual stress distribution for the circumferentially ground
model along the Y-axis (x=0). The results are shown for the coating thickness of 0.35b and
0.65b. The distribution of the residual stress σx showed a peculiar mode along the Y-axis and
it was tensile in the coated layer whereas below the coated layer, there was an abrupt change
in σx. From the figure it is clear that as the coating thickness becomes thick, the sudden
57
change in σx near the coated layer decreases. Fig 5.9 shows the distribution of residual stress
for the axially ground model at x=0 and x=0.1b for the coating thickness of 0.35b and 0.4b
respectively. From the figure it is apparent that in both these cases, there is a significant
difference in σx near the coated layer.
-0.4 -0.2 0 0.2 0.4
0
0.5
1.0
σX/PH
y/b PH=1.2GPa
µ=-0.03Circumferentiallyground modelx/b=0
: 1Pass: 3Pass: 5Pass
Boundarylayer (0.35b)
-0.4 -0.2 0 0.2 0.4σX/PH
PH=1.2GPaµ=-0.03Circumferentiallyground modelx/b=0
: 1Pass: 3Pass: 5Pass
Boundarylayer (0.65b)
Thickness=0.35b Thickness=0.65b
Fig. 5.8 Effect of coating thickness on residual stress σx
-0.4 -0.2 0 0.2 0.4
0
0.5
1.0
σX/PH
PH=1.2GPaµ=-0.03Axially groundmodelThickness=0.35b
: 1Pass: 3Pass: 5Pass
Boundarylayer (0.35b)
y/b
-0.4 -0.2 0 0.2 0.4σX/PH
PH=1.2GPaµ=-0.03Axially groundmodelThickness=0.35b
: 1Pass: 3Pass: 5Pass
Boundarylayer (0.4b)
x/b=0 x/b=0.1
Fig. 5.9 Distributions of residual stress σx
58
Figs. 5.10 and 5.11 show the calculation results of the equivalent plastic strain εpav both in
the coated layer and in the substrate layer for the same analytical conditions that were used
for the calculation of residual stresses of Figs. 5.8 and 5.9 respectively. It was found that, the
plastic strain remained almost zero in the WC cermet coated layer. For the circumferentially
ground model, Fig. 5.10 shows that with the coating thickness 0.35b, plastic strain increases
greatly below the coated layer and with the increase in the coating thickness from 0.35b to
0.65b, plastic strain decreases greatly. Fig. 5.11 shows the distribution of equivalent plastic
strain for the axially ground model. For the coating thickness of 0.35b, just below the coated
layer, the plastic strain showed lower value at x=0 as compared with that of the
circumferentially ground model of Fig. 5.10. Moreover, Fig. 5.11 shows that at x=0.1b, the
plastic strain increases below the coated layer as compared with that at x=0.
0 0.002 0.004 0.006
0
0.5
1.0
y/b
Equivalent plastic strain εpav
PH=1.2GPaµ=-0.03Circumferentiallyground modelx/b=0
: 1Pass: 3Pass: 5Pass
Boundarylayer (0.35b)
0 0.002 0.004 0.006Equivalent plastic strain εpav
PH=1.2GPaµ=-0.03Circumferentiallyground modelx/b=0
: 1Pass: 3Pass: 5Pass
Boundarylayer (0.65b)
Thickness=0.35b
Fig. 5.10 Effect of coating thickness on equivalent plastic strain εpav
Thickness=0.65b
59
Fig. 5.12 shows the distribution of equivalent plastic strain εpav along the interface layer
from x=-0.2b to +0.2b. Since the equivalent plastic strain hardly varied after 5 times pass of
loading, calculation was discontinued at 5 times pass. Calculations were performed for the
thermally refined steel substrate with the WC cermet coated layer of 0.35b under the
Hertzian stress of PH=1.2GPa. The theoretical calculations were carried out for the frictional
coefficient µ=-0.03. To emphasize the effect of frictional force on the life to flaking of coated
roller, calculations were also carried out for µ=-0.1. The equivalent plastic strains along the
interface layer for the circumferentially ground substrate and axially ground substrate are
compared. For µ=-0.03, the plastic strains show a constant value along the interface layer for
the circumferentially ground substrate whereas for the axially ground substrate, the plastic
strains show lower values except at x=±0.1b where plastic strains show slightly higher values
than those obtained for the circumferentially ground model. For frictional coefficient µ=-0.1,
0 0.002 0.004 0.006
0
0.5
1.0
Equivalent plastic strain εpav
PH=1.2GPaµ=-0.03Axially groundmodelThickness=0.35b
: 1Pass: 3Pass: 5Pass
Boundarylayer (0.35b)
y/b
0 0.002 0.004 0.006Euqivalent plastic strain εpav
PH=1.2GPaµ=-0.03Axially groundmodelThickness=0.35b
: 1Pass: 3Pass: 5Pass
Boundarylayer (0.4b)
x/b=0 x/b=0.1
Fig. 5.11 Distributions of equivalent plastic strain ε
60
the plastic strains again show a constant value along the interface layer for the
circumferentially ground substrate model but in this case, the plastic strain values are much
higher than those obtained for µ=-0.03. For the axially ground substrate model, the plastic
strains show lower values as before except at x=±0.1b where plastic strains show nearly
equal values to those obtained for the circumferentially ground model. The analytical results
suggest that in the case of thermally refined steel substrate, flaking of the coating is easy to
occur when the substrate surface is circumferentially ground and these theoretical results are
agreed well with the experimental results.
5.5 Conclusion
The effect of substrate surface finish on durability of thermally sprayed WC-Cr-Ni cermet
coating in lubricated rolling/sliding contact conditions was investigated using a two-roller
testing machine. In the experiments, WC cermet coated steel roller was mated with the
-0.2 -0.1 0 0.1 0.20
0.001
0.002
0.003
0.004
x/b
Eq
uiv
alen
t p
last
ic s
trai
n ε
pav
PH=1.2GPa, 5PassThickness=0.35bS45C thermally refined
Axiallysubstrate
Circumferentiallysubstrate
µ=-0.03: ,µ=-0.10: ,
Fig. 5.12 Distributions of equivalent plastic strain εpav along the interface layer
61
carburized steel roller without coating having a surface roughness of Ry=0.1~0.4µm in line
contact condition. The effect of substrate surface finish on the durability of cermet coating
was also analyzed by the elastic-plastic behavior of the subsurface layer. From the
experimental and theoretical results, following conclusions are drawn:
• In the case of thermally refined steel substrate, life to flaking was remarkably affected by
the substrate surface finish and the coating on the circumferentially ground substrate
showed lower durability compared with that on the axially ground substrate and blasted
substrate and this difference appeared more distinctly as the coating thickness decreased.
• Under the Hertzian stress of PH=1.4GPa, the induction hardened steel substrate rollers
showed a long life and the effects of substrate surface finish was hardly recognized
whereas the thermally refined steel substrate rollers showed a very short life even with a
coating thickness of about 210µm.
• Theoretical analysis of the elastic-plastic behavior of the subsurface layer revealed that in
the case of thermally refined steel substrate, axially ground substrate model performs
better than the circumferentially ground substrate model in order to improve the
durability of WC cermet coating when the coating thickness decreases. The analytical
results suggest that flaking of coating is easy to occur in the vicinity of the interface layer
when the substrate surface is circumferentially ground and frictional coefficient is high.
62
Chapter 6
Rolling Contact Fatigue Strength of WC Cermet
Coating under Partial EHL Conditions
6.1 Introduction
Using a two-roller testing machine, rolling contact fatigue strength of thermally sprayed WC-
Cr-Ni cermet coating was investigated under partial EHL conditions. By means of the high
energy type flame spraying (Hi-HVOF) method, the coating was formed onto the axially
ground, blasted and circumferentially ground roller specimens made of a thermally refined
carbon steel or an induction hardened carbon steel. The WC cermet coated roller finished to a
mirror-like condition was mated with the carburized and hardened rough steel roller with a
roughness of Ry=3~5µm, and a maximum Hertzian stress of PH=0.6~1.4GPa was applied in
line contact. Since the theoretical EHL minimum oil film thickness hmin was 0.1~0.7µm, the
oil film parameter Λ was less than 1 in every test. In the case of thermally refined steel
substrate, durability of coated roller under partial EHL condition was compared with the
durability of roller when the mating surface roughness was Ry≈0.2µm. Depending on the
mating surface roughness and substrate surface finish, significant differences in the durability
of coated roller were found. In the case of induction hardened steel substrate, coated rollers
exhibited a high durability under partial EHL condition and the effect of substrate surface
finish was hardly recognized. In order to discuss the durability of cermet coating, theoretical
63
analyses of elastic-plastic behavior of the subsurface layer were carried out using finite
element method. The experimental results and discussion and theoretical analyses are given
in the following sections.
6.2 Experimental Details
Experiments were carried out using a two-roller testing machine and the materials, shapes
and dimensions of the test rollers are already described in chapter 2. Table 6.1 shows a
summary of experimental results. The details of F and D rollers, the substrate surface finish,
and the WC-Cr-Ni cermet coating are also described in chapters 2 and 4.
As described already in chapter 4, in tests AA and BA, axially ground substrate rollers,
in tests AB and BB, blasted substrate rollers and in tests AC and BC, circumferentially
ground substrate rollers were used. A maximum Hertzian stress of PH=0.6~1.4GPa was
applied in line contact condition. The main results such as number of cycles N in each test
(whether flaking occurred or not), theoretical EHL minimum oil film thickness hmin,
coefficient of friction, and weight loss due to flaking and/or wear of each roller are shown in
Table 6.1.
6.3 Results and Discussion
6.3.1 Comparison of Surface Durability
As shown in Table 6.1, in the case of thermally refined steel substrate with coating thickness
of about 60 µm and under a Hertzian stress of PH=0.6GPa, in test AA-1, the axially ground
substrate roller showed a long life and continued to run up to N=2×107 cycles without any
surface distress whereas, in test AC-1, the circumferentially ground substrate roller showed a
64
short life and flaking of coating occurred at nearly N=3.4×106 cycles. In both these cases, the
experiments were continued to run under partial EHL conditions (Λ<1).
Roughness Ryd, µm
Test No.
Hardness
HVb
Thicknessc, µm
Before After
Hertz stress PH
e, GPa
Slip ratio s,%
Coefficient of friction
, µ
hmin
f, µm
(318K)
Number of cycles N, x 104
Weight loss, g
Surface damage
AA-1 F Da
777 1113/ 328
56 4.0 0.2
3.0 1.0
0.6 -14.8 0.055
~ 0.036 0.63
(1.33) 2000
0.01 0.00
F: No D: No
AA-2 F Da
759 1111/ 327
52 4.0 0.2
2.0 1.0
0.8 -14.8 0.062
~ 0.037 0.56
(1.24) 2000
0.01 0.00
F: No D: No
AB-1 F Da
786 1090/ 330
54 4.0 0.2
6.0 3.0
0.8 -14.8 0.067
~ 0.035 0.54
(1.24) 1197
0.07 0.08
F: No D: Flaking
AB-2 F Da
789 1115/ 330
106 4.0 0.1
3.0 1.0
0.8 -14.8 0.065
~ 0.034 0.63
(1.24) 2000
0.02 0.01
F: No D: No
AC-1 F Da
779 1151/ 318
67 5.0 0.1
8.0 2.0
0.6 -14.8 0.057
~ 0.034 0.53
(1.33) 342
0.08 0.11
F: No D: Flaking
AC-2 F Da
789 1124/ 304
63 5.0 0.1
10.0 3.0
0.8 -14.8 0.065
~ 0.038 0.54
(1.24) 25
0.13 0.23
F: No D: Flaking
AC-3 F Da
853 1128/ 332
107 4.0 0.1
2.0 1.0
0.8 -14.8 0.063
~ 0.035 0.74
(1.24) 2000
0.01 0.01
F: No D: No
BA-1 F Da
816 1131/ 684
61 3.0 0.1
2.0 1.0
1.4 -28. 0 0.050
~ 0.032 0.18
(1.03) 2000
0.02 0.02
F: No D: No
BA-2 F Da
774 1080/ 703
67 5.0 0.1
3.0 1.5
1.4 -28.0 0.049
~ 0.036 0.13
(1.03) 2000
0.02 0.01
F: No D: No
BB-1 F Da
749 1140/ 733
52 3.0 0.2
2.0 3.0
1.4 -28.0 0.042
~ 0.031 0.18
(1.03) 2000
0.01 0.01
F: No D: No
BB-2 F Da
818 1027/ 678
55 5.0 0.1
3.0 2.0
1.4 -28.0 0.054
~ 0.036 0.14
(1.03) 2000
0.01 0.01
F: No D: No
BC-1 F Da
803 1115/ 704
52 3.0 0.2
2.0 2.0
1.4 -28.0 0.054
~ 0.047 0.13
(1.03) 2000
0.02 0.03
F: No D: No
BC-2 F Da
788 1137/ 692
50 4.0 0.1
3.0 3.0
1.4 -28.0 0.056
~ 0.035 0.17
(1.03) 2000
0.04 0.01
F: No D: No
BC-3 F Da
807 1001/ 669
58 5.0 0.1
2.0 2.0
1.4 -28.0 0.051
~ 0.039 0.16
(1.03) 2000
0.09 0.09
F: No D: Flaking
BC-4 F Da
817 1132/ 714
113 5.0 0.1
3.0 2.0
1.4 -28.0 0.051
~ 0.038 0.16
(1.03) 2000
0.02 0.02
F: No D: No
aWC/CrNi cermet coated roller by Hi-HVOF. bSurface hardness of F roller and coating hardness / substrate hardness of coated D roller. cThickness of coating. dRy: maximum height of the profile according to ISO 4287-1997 and JIS B 0601-1994 (sampling length 0.25mm). ePH: maximum Hertzian stress. fhmin: EHL minimum oil film thickness calculated using the oil viscosity at roller surface temperature. ( ) is hmin for the inlet oil temperature 45oC (318K).
Table 6.1 Summary of experiments and main results
65
Fig. 6.1 shows the effect of mating surface roughness on life to flaking in the case of
thermally refined steel substrate. The durability of coated roller is shown when the mating
surface roughness was RyF≈0.2µm ( data from Table 5.1 of chapter 5) and compared with
the durability or life to flaking of coated roller under partial EHL condition. From the
comparison, it is clear that in the case of axially ground substrate, durability of coated roller
is not influenced by the mating surface roughness. On the other hand, in the case of blasted
and circumferentially ground substrate, mating surface roughness has significant effect on the
life to flaking of coated roller. Namely, for blasted substrate surface, flaking of coating
occurred at N=1.2×107 cycles when the mating surface roughness was RyF≈4µm whereas the
coated roller exhibited a fairly long life up to N=2×107 cycles without any surface distress
when the mating surface roughness was RyF≈0.2µm. In the case of circumferentially ground
substrate, mating surface roughness affects the flaking life significantly. Under partial EHL
condition, flaking of coating occurred at N=2.5×105 cycles which is remarkably shorter as
compared to the flaking life of N=1.0×107 cycles when the mating surface roughness was
RyF≈0.2µm.
From Table 6.1, it is apparent that in the case of induction hardened steel substrate, coated
rollers exhibited a long life up to N=2×107 cycles under partial EHL condition (Λ<1) and life
to flaking was hardly affected by the substrate surface finish.
66
Fig. 6.2 shows the external views of the flaking that occurred on the coated D roller
surfaces in the case of thermally refined steel substrate under partial EHL condition. It seems
that under partial EHL condition, in all the cases flaking originated from near the track end
and spread rapidly over the contact area. Fig. 6.3 shows the results of depth of flaking and
from these results it is clear that in all the cases, depth of flaking was nearly equal to the
coating thickness and along the interface layer.
AxiallyBlasted
Circum-
1.0GPa
0.8GPa
N=2.0×107
N=2.0×107
N=1.0×107N=2.0×107
N=1.2×107
N=2.5×105
1.0E+04
5.0E+06
1.0E+07
1.5E+07
2.0E+07
Nu
mb
er o
f cy
cles
PH
s=-14.8%
ground
ferentially ground
(RyF≒4µm)
(RyF≒0.2µm)
Fig. 6.1 Effect of mating surface roughness on life to flaking (Thermally refined steel, Thickness≈60 µm)
67
Table 6.1 shows the surface roughness of F roller and coated D roller before and after the
test. Since the surface roughness of F roller was many times greater than the oil film
Fig. 6.2 External views of flaked surfaces
Exp.AC-1PH=0.6GPa
N=342×104
Exp.AC-2PH=0.8GPa
N=25×104
Exp.AB-1PH=0.8GPa
N=1197×104
0
20
40
60
80
100
Circum-ferentially
ground
Circum-ferentially
ground
Blasted
Dep
th o
f fl
akin
g, µ
m
Coatingthickness
Coatingthickness
Fig. 6.3 Depth of flaking (Thermally refined steel: s=-14.8%, Thickness≈60µm)
68
thickness, the oil film parameter Λ was less than 1 in every test. Fig. 6.4 shows the profile
curves of the mating surfaces for the tests AA-1, BA-2 and BC-4. From these profile curves,
it is clear that after the test, the surface roughness of F roller was decreased and D roller was
increased. From Table 6.1, it can be seen that in the tests where flaking of coating occurred
and the testing machine was stopped before N=2×107 cycles, after the test, the surface
roughness of both F and D rollers was increased remarkably. Otherwise, the tests continued
up to N=2×107 cycles, after the test, the surface roughness of F roller was decreased and D
roller was increased.
Fig. 6.4 Profile curves of mating surfaces in axial direction
69
6.3.2 States of Oil Film Formation and Friction
Fig. 6.5 shows some results of the measurement of the state of oil film formation between
rollers. For fully developed oil film, the voltage Eab recorded on a chart shows 15 mV.
Under partial EHL condition (Λ<1), results of the tests AA-2, AB-1, and AC-2 are shown. It
is apparent from the figure that immediately after the start of running, the voltage was very
near to zero or a very low value due to the severe asperity contacts, then the voltage rose very
steadily with the number of cycles. These results are compared with the results obtained for
the mating surface roughness RyF≈0.2µm in tests AA-1, AB-1 and AC-1 (Table 5.1 of
chapter 5) where oil film started to develop quickly from the start of running. From the figure
it is apparent that there is a significant difference in the states of oil film formation depending
on the mating surface roughness.
104 105 106 1070
5
10
15
Number of cycles, N
Vo
ltag
e E
ab, m
V
2×107
: BlastedRyF=0.1µmPH=1GPa
AxiallyRyF=4µmPH=0.8GPa
Circum-ferentiallyRyF=5µmPH=0.8GPa
BlastedRyF=4µmPH=0.8GPa
Circum-ferentiallyRyF=0.2µmPH=1GPa
AxiallyRyF=0.2µmPH=1GPa
Fig. 6.5 Oil film formation between rollers (Thermally refined, Eab=0mV: Contact, 15mV: Separation)
70
Table 6.1 shows the results of friction measurement in each test as the coefficient of
friction (initial value ~ steady value). Fig. 6.6 shows a comparison of the coefficient of
friction of the tests that show the oil film formation in Fig. 6.5. These results show almost the
same tendency as that of oil film formation. From the figure it is clear that at the initial stage
of running, there is a significant difference in the coefficient of friction depending on the
mating surface roughness. Under partial EHL condition (Λ<1) where the mating surface
roughness was RyF≈4µm, at the start of running, the coefficient of friction was very high due
to the severe asperity contacts and it decreased rapidly with the number of cycles and came to
a steady value. On the other hand, in the case of mating surface roughness RyF≈0.2µm, at the
start of running, the coefficient of friction showed much lower values than those obtained for
Λ<1.
0 1 2 3 4 5 6
[×104]
0
0.02
0.04
0.06
0.08
0.10
Number of cycles N
Co
effi
cien
t o
f fr
icti
on
µ RyF≒0.2µm,PH=1.0GPa●:Axially▲:Blasted■:Circumferentially
RyF≒4µm,PH=0.8GPa:Axially:Blasted:Circumferentially
Fig. 6.6 Changes in coefficient of friction (Thermally refined)
71
6.4 Elastic-Plastic Analysis
Taking into consideration the results obtained from the experimental investigation,
theoretical analyses of the elastic-plastic behavior of the subsurface layer under repeated
rolling with sliding contact loads were carried out using a finite element method (FEM). In
view of the fact that in the case of thermally refined steel substrate, the life to flaking of the
coated roller was significantly affected by the substrate surface finish, theoretical calculations
were carried out using the circumferentially ground model and axially ground model. The
effects of friction, coating thickness, and substrate hardness on the residual stress and
equivalent plastic strain were calculated. The analytic domain used for the FEM analysis has
been described in chapter 3. The analytic model, the analytical conditions, details of the
analytic space, material parameters and the calculated results have been discussed in the
following section. The circumferentially ground model and the axially ground model are
shown in Figs. 6.7a and 6.7b.
In the FEM analysis, the plane strain quadrangular element with eight nodal points and the
plane strain triangular element with six nodal points were used. The incremental theory for
plastic deformation and the isotropic hardening rule was applied to the plastic deformation of
the material. As a criterion for yielding of the elements, the von Mises’ yield criterion was
used. The boundary conditions were adopted in the same way as the previous investigation
by Nakajima et al. (38-39). The dimensions of the finite element model are as follows:
The analytic space: 140b х 60b (width х depth)
The number of elements: 3100 (circumferentially ground model)
The number of nodal points: 9563 (circumferentially ground model)
The number of elements: 3200 (axially ground model)
The number of nodal points: 9663 (axially ground model)
72
The smallest element: 0.1b х 0.05b (width х depth)
The same way as the previous investigation by Ishikawa et al. (50-51), calculations were
performed for the maximum Hertzian stress of PH=1.0GPa and PH=1.4GPa. Under
PH=1.0GPa, the coating thickness 0.25b and 0.45b corresponds to 66µm and 119µm
respectively. Under PH=1.4GPa, the coating thickness 0.15b corresponds to 56µm.
Calculations were carried out for the frictional coefficient µ=-0.03, -0.06, and -0.1. Where,
the sign of µ defined as negative when the directions of friction force and load movement are
opposed to each other. Table 6.2 shows the material parameters used in the numerical
calculations.
Fig. 6.7a Circumferentially ground model
Fig. 6.7b Axially ground model
73
Table 6.2 Material parameters
Substrate material Material
WC-CrNi Low hardness High hardness
Young’s modulus E, GPa 432 206 206 Poisson’s ratio ν 0.3 0.3 0.3 Yield stress σY , MPa 2060 294 1030 Shear yield stress k, MPa 1189 170 595 Tangent modulus H’, GPa 206 20.6 103
Figs. 6.8 and 6.9 show the calculation results of the distribution of residual stress σx both
in the coated layer and in the substrate layer. In the numerical calculations, since the residual
stress hardly varied after 5 times pass of loading, the calculation was discontinued at 5 times
pass. Fig. 6.8 shows the distribution of residual stress σx in the case of low hardness substrate.
Calculations were carried out for Hertzian stress of PH=1.0GPa. Fig. 6.8(a) shows the effect
of friction on residual stress distribution for the circumferentially ground model along the Y-
axis (x=0) and for the coating thickness 0.25b. Calculations were carried out for µ=-0.03, -
0.06, and -0.1. The distribution of the residual stress σx showed a peculiar mode along the Y-
axis and it was tensile in the coated layer whereas below the coated layer, there was an abrupt
change in σx. Fig. 6.8(b) shows the effect of coating thickness on residual stress distribution
for the circumferentially ground model along the Y-axis (x=0) and for µ=-0.06. Calculations
were carried out for the coating thickness 0.25b and 0.45b. From the figure it is clear that as
the coating thickness becomes thick, the sudden change in σx near the coated layer decreases.
Fig. 6.8(c) shows the distribution of residual stress for the axially ground model at x=0 and
x=0.1b for the coating thickness 0.25b and 0.3b respectively. Calculations were carried out
for µ=-0.06. The distributions of residual stress show almost the same value at x=0 and
x=0.1b. Fig. 6.9 shows the effect of substrate hardness on residual stress σx for the
circumferentially ground model. In order to emphasize the effect of the frictional force on the
74
life to flaking of coated roller, calculations were performed for the frictional coefficient µ=-
0.1. The residual stress calculations were carried out for Hertzian stress of PH=1.4GPa and
the coating thickness was fixed at 0.15b which corresponds to 56µm. From the figure it is
apparent that in the case of low hardness substrate, high pressure and high friction
significantly affects the residual stress distribution in the subsurface layer along the Y-axis
whereas in the case of high hardness substrate, the residual stress hardly changed in the
subsurface layer.
-1.0 -0.5 0 0.5 1.0σX/PH
PH=1.0GPaµ=-0.06Axially groundmodel, 5PassThickness=0.25b
: x/b=0: x/b=0.1
Boundarylayer (0.25b)
Boundarylayer(0.3b)
-1.0 -0.5 0 0.5 1.0σX/PH
Boundarylayer (0.25b)
PH=1.0GPaµ=-0.06Circumferentiallyground modelx/b=0, 5PassThickness
: 0.25b: 0.45b
Boundarylayer(0.45b)
-1.0 -0.5 0 0.5 1.0
0
0.5
1.0
σX/PH
y/b
Boundarylayer (0.25b)
PH=1.0GPaCircumferentiallyground modelx/b=05Pass
: µ=-0.03: µ=-0.06: µ=-0.10
(a) Effect of friction (b) Effect of thickness (c) Axially ground model
Fig. 6.8 Distributions of residual stress σx (Low hardness substrate)
-1.5 -1.0 -0.5 0 0.5 1.0 1.5
0
0.5
1.0
σX/PH
PH=1.4GPaµ=-0.1Circumferentiallyground modelThickness=0.15b5Pass
Boundarylayer(0.15b)
y/b
Lowhardnesssubstrate
High hardnesssubstrate
Fig. 6.9 Effect of substrate hardness on residual stress σx
75
Figs. 6.10 and 6.11 show the calculation results of the equivalent plastic strain εpav both in
the coated layer and in the substrate layer for the same analytical conditions that were used
for the calculation of residual stresses of Figs 6.8 and 6.9 respectively. It was found that, the
plastic strain remained almost zero in the WC cermet coated layer. Fig. 6.10(a) shows that in
the case of low hardness substrate and for the circumferentially ground model, friction plays
a dominant role in the distribution of equivalent plastic strain and the plastic strain increases
greatly just below the coated layer as the coefficient of friction increases. Fig. 6.10(b) shows
that for the circumferentially ground model, below the coated layer, the plastic strain
increases greatly as the coating thickness decreases. Fig 6.10(c) shows the distribution of
equivalent plastic strain for the axially ground model at x=0 and x=0.1b. From the figure it
can be seen that below the coated layer, the plastic strain shows lower value at x=0 as
compared with that of the circumferentially ground model of Fig. 6.10(a). Moreover, there is
a difference in the plastic strain values at x=0 and x=0.1b. Fig. 6.11 illustrates the effect of
substrate hardness on the distribution of equivalent plastic strain εpav for the circumferentially
ground model. From the figure it is very clear that in the case of low hardness substrate and
for Hertzian stress of PH=1.4GPa and frictional coefficient µ=-0.1, below the coated layer,
the equivalent plastic strain shows an extremely high value. On the other hand, the equivalent
plastic strain remained almost zero in the case of high hardness substrate. Consequently, it is
concluded that higher hardness substrate is effective to improve the durability of WC cermet
coating.
76
Fig. 6.12 shows the distribution of equivalent plastic strain εpav along the interface layer
from x=-0.2b to +0.2b. Since the equivalent plastic strain hardly varied after 5 times pass of
loading, calculation was discontinued at 5 times pass. The theoretical calculations were
performed for the low hardness substrate with the coating thickness 0.25b corresponds to
0 0.005 0.010 0.015
0
0.2
0.4
0.6
0.8
1.0
y/b
Equivalent plastic strain εpav
PH=1.0GPaCircumferentiallyground modelx/b=05Pass
: µ=-0.03: µ=-0.06: µ=-0.10
Boundarylayer (0.25b)
0 0.005 0.010 0.015Equivalent plastic strain εpav
PH=1.0GPaµ=-0.06Circumferentiallyground modelx/b=0, 5PassThickness
: 0.25b: 0.45b
Boundarylayer (0.25b)
Boundarylayer (0.45b)
0 0.005 0.010 0.015Equivalent plastic strain εpav
PH=1.0GPaµ=-0.06Axially groundmodel, 5PassThickness=0.25b
: x/b=0: x/b=0.1
Boundarylayer (0.25b)
Boundarylayer(0.3b)
(a) Effect of friction (b) Effect of thickness (c) Axially ground model
0 0.010 0.020
0
0.2
0.4
0.6
0.8
1.0
y/b
Equivalent plastic strain εpav
PH=1.4GPaµ=-0.1Circumferentiallyground modelThickness=0.15b5Pass
Boundarylayer (0.15b)
Highhardnesssubstrate
Low hardnesssubstrate
Fig. 6.10 Distributions of equivalent plastic strain εpav (Low hardness substrate)
Fig. 6.11 Effect of substrate hardness on equivalent plastic strain εpav
77
66µm under the Hertzian stress of PH=1.0GPa. Calculations were carried out for the frictional
coefficient µ=-0.06. The equivalent plastic strains along the interface layer for the
circumferentially ground substrate and axially ground substrate are compared. From the
figure, it is apparent that the plastic strains show a constant value along the interface layer for
the circumferentially ground substrate whereas for the axially ground substrate, the plastic
strains show lower values than those obtained for the circumferentially ground substrate
except at x=±0.1b. At x=±0.1b, the plastic strains for axially ground substrate are nearly
equal to those for the circumferentially ground substrate. These analytical results suggest that
in the case of low hardness substrate, susceptibility of flaking of WC cermet coating is
extremely high in the vicinity of the interface layer if the substrate surface is
circumferentially ground and these theoretical results are agreed well with the experimental
results.
-0.2 -0.1 0 0.1 0.20
0.001
0.002
0.003
0.004
0.005
0.006
x/b
Eq
uiv
alen
t p
last
ic s
trai
n ε
pav
PH=1.0GPa, µ=-0.06Thickness=0.25bLow hardness substrate5Pass
Axiallysubstrate
Circumferentiallysubstrate
Fig. 6.12 Distributions of equivalent plastic strain εpav along the interface layer
78
6.5 Conclusion
Using a two-roller testing machine, rolling contact fatigue strength of thermally sprayed WC
cermet coating was investigated in partial EHL condition (Λ<1). Durability of the coated
roller under partial EHL condition was compared with the durability of the coated roller
when the mating surface roughness was Ry≈0.2µm. In order to discuss the durability of WC
cermet coating, theoretical analyses of the elastic-plastic behavior of subsurface layer were
also carried out. From the experimental and theoretical results, following conclusions are
drawn:
• In the case of thermally refined steel substrate, durability of coated roller was not
influenced by the mating surface roughness when the substrate surface was axially
ground whereas, durability of coated roller was significantly influenced when the
substrate surface was blasted or circumferentially ground. In particular, for the
circumferentially ground substrate, the durability of the coated roller was remarkably
shorter under partial EHL condition as compared to the durability of the coated roller
when the mating surface roughness was Ry≈0.2µm.
• From the theoretical analysis of the elastic-plastic behavior of the subsurface layer, it was
found that in the case of low hardness substrate, Hertzian stress and friction play a
dominant role in the distribution of plastic strain when the substrate surface is
circumferentially ground. The analytical results suggest that in the case of low hardness
substrate, flaking of WC cermet coating is very easy to occur in the vicinity of the
interface layer if the substrate surface is circumferentially ground. Moreover, from the
theoretical results it is concluded that high hardness substrate is effective to improve the
79
durability of WC cermet coating and these results are agreed well with the experimental
results.
80
Chapter 7
Concluding Remarks and Subjects for Future
Research
Rolling contact fatigue (RCF) is responsible for the failure of machine elements such as
rolling element bearings, gears, cams and tappets and defined as cracking, or pitting, or
spalling/flaking limited to the surface or near-surface layer of the components under repeated
rolling/sliding contact. In order to achieve better use properties of the materials, surface
modification technologies are going with a remarkable progress for the purpose of improved
rolling contact fatigue life of machine elements. In recent years, the strongest demand has
been for wear-resistant coating materials particularly tungsten carbide (WC) based cermets
for enhancing the surface characteristics of a material or extending its service life under
severe tribological and environmental constraints. In order to achieve enhanced tribological
performance, cermet coating must remain firmly attached to the substrate. Substrate surface
finish and substrate material actively play vital role in the degree of adhesion of coating to
the substrate which in turn may affect significantly the rolling contact fatigue life of machine
elements. Therefore, how substrate surface finish and substrate material affect the durability
of WC cermet coating under rolling/sliding contact condition was the main objective of this
study. Moreover, the effects of friction, coating thickness, contact pressure, and mating
surface roughness on the durability of WC cermet coating were taken into consideration in
this study.
81
This study primarily investigates the effects of substrate surface finish and substrate
material on durability of thermally sprayed WC-Cr-Ni cermet coating under rolling/sliding
contact. The coated roller finished to mirror-like condition was mated with the rough
carburized steel roller without coating having surface roughness of Ry=3.0~5.0µm. It was
found that in the case of thermally refined steel substrate, life to flaking was remarkably
affected by the substrate surface finish, namely, axially ground substrate roller showed a long
life whereas, durability of coated roller was lowered when the substrate surface was blasted
or circumferentially ground, particularly, circumferentially ground substrate roller showed a
very short life. In the case of induction hardened steel substrate, coated roller exhibited a
long life and life to flaking was hardly affected by the substrate surface finish. Theoretical
calculations showed that rough substrate surface performs better than smooth substrate
surface to improve the durability of coated roller when the coating thickness becomes thin in
the lower hardness substrate such as thermally refined steel. Experimental investigations
were also carried out when the mating surface was smooth with surface roughness of
Ry=0.1~0.4µm. In the case of thermally refined steel substrate, the coating on the
circumferentially ground substrate generally showed a lower durability compared with that
on the axially ground substrate or blasted substrate, and this difference appeared more
distinctly as the coating thickness decreased. On the other hand, the induction hardened steel
substrate roller showed a higher durability, and the effect of substrate surface finish was
hardly recognized. Theoretical analysis revealed that in the case of thermally refined steel
substrate, flaking of coating is easy to occur in the vicinity of the interface layer when the
substrate surface is circumferentially ground and frictional coefficient is high. Finally, rolling
contact fatigue strength of cermet coating was investigated under partial EHL condition
(Λ<1). In the case of thermally refined steel substrate, depending on the mating surface
82
roughness and substrate surface finish, significant differences in the durability of coated
roller were found. Theoretical analysis revealed that in the case of low hardness substrate,
under Hertzian stress of PH=1.4GPa and for frictional coefficient µ=-0.1, plastic strain shows
an extremely high value below the coated layer when the substrate surface is
circumferentially ground. From the obtained results it is concluded that in the case of low
hardness substrate, flaking of WC cermet coating is very easy to occur in the vicinity of the
interface layer when the substrate surface is circumferentially ground. It is also concluded
that high hardness substrate is effective to improve the durability of WC cermet coating.
Recently, durability of thermally sprayed WC cermet coating under rolling/sliding contact
conditions has been the study of much investigation. There is an increased demand for
improved life and load bearing capacity of bearing materials and future applications will
demand their use in more severe operating conditions such as extremely high pressure, very
high speed, high surface traction and high operating temperature. Therefore, durability of
WC cermet coating need to be investigated in more severe operating conditions. Moreover,
to understand the durability of WC cermet coating more clearly with different substrate
material under extreme operating conditions, experimental and theoretical investigations also
need to be carried out in the case of higher hardness substrate such as carburized hardened
steel and a comparison can be made with the induction hardened steel and the thermally
refined steel substrate cases.
Under very high pressure, high friction and with rough mating surface, experimental
investigations need to be carried out using the anti-wear (extreme pressure) lubricant to
understand the effect of lubricating oils on the durability of WC cermet coating under partial
EHL condition.
83
It is also desirable that durability of WC cermet coating in dry contact condition will be
investigated and a comparison can be made with that of the lubricated contact case.
84
Acknowledgement
First, I gratefully acknowledge my sincere veneration and indebtedness and express my
profound gratitude and deep respect to my supervisor Dr. Akira Nakajima, Professor,
Department of Mechanical Engineering, Saga University, for his valuable guidance,
suggestions, and encouragement throughout all phases of this research work. It is also a great
honor and privilege for me to work with my supervisor and to share his valuable knowledge
and expertise.
I also wish to pay my gratefulness to Mr. Toshifumi Mawatari, Research Associate,
Department of Mechanical Engineering, Saga University, for his helpful supports and
valuable suggestions during my research work. I am greatly indebted to him for his sincere
support and technical assistance during my study.
I also wish to pay my gratefulness to all the members of the committee, Prof. Dr. Hidehiro
Yoshino, Prof. Dr. Nobuyoshi Ohno and Assoc. Prof. Dr. Bo Zhang for their encouragement
and suggestions during this research. I deeply thank all of them for their valuable comments
and suggestions.
I would like to thank my lab-mates for their continuous help during this research work,
particularly, Mr. Hajime Yoshida, who helped me a lot during my study. I am very grateful to
all of my friends for their encouragement and help during my stay in Saga.
I am indebted forever to my parents for their support in all respects. I wish to remember
my wife Zeenatul Kubra for her love, encouragement, and patience who partially missed my
accompany and sacrificed a lot during this research work. I also remember my son Dewan
Najmus Saqib, who also missed my love and accompany.
85
I would like to express my gratitude and thanks to the staffs of Tocalo Company Ltd., for
providing thermally sprayed test rollers.
Finally, the financial support in the form of Monbukagakusho Scholarship provided by the
Ministry of Education, Culture, Sports, Science and Technology, Government of Japan, to
carry out this research work is gratefully acknowledged.
86
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92
Appendix A
Formulations of Oil Film Thickness, Load and Oil
Film Parameter
Mathematical Formulation of Oil Film Thickness
Dowson and Higginson’s power law equation was adopted to calculate the theoretical EHL
minimum oil film thickness which is as follows:
( ) RRbE
P
RE
uEhor
WUGR
h
13.07.0
054.0min
13.07.054.0min
65.2,
65.2
−
−
⎟⎠
⎞⎜⎝
⎛
′⎟⎠
⎞⎜⎝
⎛
′′=
=
ηα [A1]
where,
hmin : theoretical EHL minimum oil film thickness
R : reduced radius of the contacting solids
material parameter : EG ′=α [A2]
speed parameter : RE
uU
′= 0η
[A3]
load parameter : RbE
PW
′= [A4]
The component parameters of WandUG ,, are described as:
α : pressure-viscosity coefficient, GPa-1
E ′ : reduced elastic modulus, GPa
93
0η : lubricant viscosity at atmospheric pressure, Pa.s
u : average surface speed of the contacting solids, mm/s
P : applied load, N
b : contact width, mm
The reduced radius of the contacting solids, R is defined as,
21
111
RRR+= [A5]
where, 21 , RR : radius of the contacting solids
The reduced elastic modulus E ′ is defined as,
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −+
−=
′ 2
22
1
21 11
2
11
EEE
νν [A6]
where, 21,νν : poisson’s ratio of the contacting solids
21, EE : elastic modulus of the contacting solids
lubricant viscosity at atmospheric pressure, 0η is defined as,
νγη ×=0 [A7]
for, Mobil DTE Oil Heavy Medium VG68,
the specific gravity, γ is defined as,
( ){ } 60 108778.01500064.0 −×+−×−= Ctγ [A8]
the kinematic viscosity, ν is defined as,
7.010)15.273(log5798.31905.9
10 −= ⎭⎬⎫
⎩⎨⎧ +×− t
ν [A9]
and the pressure-viscosity coefficient, α is defined as,
να log6293.38049.6 ×+= [A10]
the average surface speed of the contacting solids is calculated by,
94
{ }
⎭⎬⎫
⎩⎨⎧
+=
+×=
+=
12
1211
2211
21
60
602
12
nz
zRnR
ndnd
uuu
π
π [A11]
where, 1n is the driving side speed, rpm
and 2
1
z
z is the gear ratio
Load Calculation
Maximum Hertzian stress PH is defined as,
⎭⎬⎫
⎩⎨⎧
−+−×
+×=
12
222
1
21
21
212
)1()1( EE
EE
RR
RR
b
PPH ννπ
[A12]
Therefore, ⎭⎬⎫
⎩⎨⎧
−+−×
+×=
12
222
1
21
21
21
)1()1( EE
EE
RR
RR
b
PPH ννπ
[A13]
so that, 2
21
212 )1(2
HPRR
RR
E
bP ×
+×−= νπ
[A14]
where, 3.021 === ννν and 20621 === EEE GPa
Oil Film Parameter
The oil film parameter Λ is defined as,
Λ = 2
122
min
)(21 rmsrms RR
h
+ [A15]
where, rmsR is the root mean square (RMS) surface roughness.
For EHL contact, Λ>3 and for partial EHL contact, Λ<1.
95
Appendix B
Theoretical Basis of Line Loading of an Elastic
Half-Space
The Elastic Half-Space
Non-conforming elastic bodies in contact whose deformation is sufficiently small make
contact over an area which is generally small compared with the dimensions of the bodies
themselves. The stresses are highly concentrated in the region close to the contact zone and
are not greatly influenced by the shape of the bodies at a distance from the contact area. The
stresses are calculated to good approximation by considering each body as a semi-infinite
elastic solid bounded by the plane surface i.e. an elastic half-space.
In the following section, theoretical basis of stresses and deformations in an elastic half-
space loaded over a narrow strip (line loading) will be discussed. An elastic half-space
loaded over the strip from x=-b to x=a by a normal pressure p(x) and tangential traction f(x)
distributed in any arbitrary manner is shown in Fig. B1 while the remainder of the surface is
free from traction. The boundary surface is the x-y plane and the z-axis is directed into the
solid. It is assumed that a state of plane strain (εy=0) is produced in the half-space by the line
loading. It is aimed at finding the stress components σx, σz and τxz due to p(x) and f(x) at any
point A in the body of the solid and the components ux and uz of the elastic displacement of
any point C on the surface of the solid.
96
The stress components must satisfy the equilibrium equations which is as follows:
⎪⎪⎭
⎪⎪⎬
⎫
=∂
∂+
∂∂
=∂
∂+
∂∂
0
0
xz
zx
xzz
xzx
τσ
τσ
[B1]
The corresponding strains εx, εz and εxz must satisfy the compatibility condition:
zxxzxzzx
∂∂∂
=∂∂
+∂
∂ γεε 2
2
2
2
2
[B2]
where the strains are related to the displacements by,
z
u
x
u
z
u
x
u zxxz
zz
xx ∂
∂+
∂∂
=∂
∂=
∂∂
= γεε ,, [B3]
Under conditions of plane strain,
)(
0
zxy
y
σσνσε
+=
= [B4]
ds
z
x
p(s)
f(s)
s
uz
ux
A(x,z)
b a
O B C(x,0)
Fig. B1 Elastic half-space loaded by normal pressure and tangential traction
97
whereupon Hooke’s law, relating the stresses to the strains, may be written:
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
+==
+−−=
+−−=
xzxzxz
xzz
zxx
EG
E
E
τντγ
σννσνε
σννσνε
)1(21
})1()1({1
})1()1({1
2
2
[B5]
The tractions acting on the surface at B, distance s from O, on an elemental area of width ds
are regarded as concentrated forces of magnitude pds acting normal to the surface and fds
acting tangential to the surface. The stresses at A(x,z) due to these forces are integrated over
the loaded region to give the stress components at A due to the complete distribution of p(x)
and f(x). Therefore,
∫∫ −− +−−−
+−−−=
a
b
a
bxzsx
dssxsf
zsx
dssxspz222
3
222
2
}){(
))((2
}){(
))((2
ππσ [B6]
∫∫ −− +−−−
+−−=
a
b
a
bzzsx
dssxsfz
zsx
dsspz222
2
222
3
}){(
))((2
}){(
)(2
ππσ [B7]
∫∫ −− +−−−
+−−−=
a
b
a
bxzzsx
dssxsfz
zsx
dssxspz222
2
222
2
}){(
))((2
}){(
))((2
ππτ [B8]
Denoting the tangential and normal displacement of point C(x,0) due to the combined action
of p(x) and f(x) by xu and zu respectively, the displacement gradients at the surface
xu x ∂∂ / and xu z ∂∂ / are expressed as:
dssx
sf
Exp
Ex
u a
b
x
∫− −−−+−−=
∂∂ )()1(2
)()1)(21( 2
πννν
[B9]
)()1)(21()()1(2 2
xfE
dssx
sp
Ex
u a
b
z ννπ
ν +−+−
−−=∂
∂∫−
[B10]
The gradient xu x ∂∂ / is recognized as the tangential component of strain xε at the surface
and the gradient xu z ∂∂ / is the slope of the deformed surface.
98
Due to the normal pressure p(x) alone, equation [B9] reduces to:
)()1)(21(
xpEx
u xx
ννε +−−=∂
∂= [B11]
But, from Hooke’s law in plane strain, at the boundary, from equation [B5],
})1()1{(1 2
zxxE
σννσνε +−−= [B12]
As )(xpz −=σ , and equating the two expressions for xε ,
)(xpzx −==σσ [B13]
Thus, under any distribution of surface pressure, the tangential and normal direct stresses at
the surface are compressive and equal which restricts the tendency of the surface layer to
yield plastically under a normal contact pressure. The above equations are the basis of the
two-dimensional Hertzian contact of cylindrical bodies.