TRIBOLOGICAL ANALYSIS OF INJECTION CAMS LUBRICATION

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TRIBOLOGICAL ANALYSIS OF INJECTION CAMS LUBRICATION

IN ORDER TO REDUCE FRICTION & WEAR

av

Julien Claret-Tournier •••• 2007 06 21

Handledare : M. Frederic Cabanettes Examinator : Pr. Bengt-Göran Rosén

Ett examensarbete utfört enligt kraven för Högskolan i Halmstad

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Abstract

Engine development is now driven by cost, performance, governmental regulations and customer demands. Several of the requirements have tribological associations. Tribo- logical improvements which consist in lowering friction and improving wear resistance in engines, will play a major role to increase reliability and life cycle.

The components studied here are parts of the valvetrain mechanism of heavy-duty Diesel engines. The injection cam is one of the most problematic parts of the camshaft, as it is subjected to high pressures from the fuel injector. Lubrication is of significant importance in the prevention of cam failure caused by wear. However, the satisfactory lubrication of the cam and roller contact has proved to be one of the most difficult tribo- logical design challenges to take up.

For a lubricated contact, the degree of separation between surfaces has a very strong influence on the type and amount of wear. This degree of separation is termed as specific film thickness ; its value provides a measure of the severity of asperities interaction in the lubricated contact.

In this report, attention is drawn on the evaluation of oil film thickness in the cam-roller contact, in order to predict regimes of lubrication and thus to identify the probable wear zones of the injection cam. Then, confrontation with experimental results is performed (observation of worn cam surfaces). Future work to achieve is to discover the influence of the different parameters on oil film thickness, by performing a multivariate analysis.

The next step will focus on modelling the wear of injection cams, and finally establishing quantified correlations between wear and specific film thickness.

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Acknowledgements

I want to thank all the people who helped me to carry out this final-year-project and so to go trough this experience in Sweden. My thanks go to the following persons :

Pr. Bengt-G¨ oran Ros´ en for his warm welcome to the University of Halmstad, his kindness, and for his confidence on me to carry out this project.

Mr. Frederic Cabanettes, who helped me to follow-up my project, for his suggestions and comments, and the time he dedicated me always in a good mood.

Mr. Zlate Dimkovski, Peter Larsson, P¨ ar-Johan L¨ o¨ of and Mathias Pettersson, our colleagues, for their help and their company.

Mr. Stefan Ros´ en from Toponova AB for his instructions and guidance in performing optimal measurements on the profilometer.

Mrs. Li Xiao and Mr. Johan Mohlin respectively from Volvo Powertrain Corporation and Finnveden Powertrain AB, for their cooperation and all the meaningful data they provided me, which helped to carry out my project successfully.

To finish, big up to all the exchange students from all over the world I met during this period, who made this human experience unforgettable. Thank you for this awesome semester.

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Nomenclature

A kinematic parameter A = 2 ·

^(u_(u²^−u¹⁾

2+u1)

b semi-length of contact b along the x axis, m

b =

q

8·w·Rx

π·L·E⁰

Br Brinkman number

Br = −

_∂T^∂η

·

^u^¯_K²

≈

^β·η_K⁰^·¯^u²

C

_T

dimensionless thermal correction factor

E

⁰

effective modulus of elasticity, Pa E

⁰

= 2 ·

_1−ν2 1

E1

+

^1−ν_E ²²

2

−1

E

_i

modulus of elasticity of the mate- rial i, Pa

F tangential force exerted by fric- tion, N

G dimensionless material parameter G = α · E

⁰

h

₀

central film thickness, µm h

_min

minimum film thickness, µm K thermal conductivity of the lubri-

cant, W /m ·

^◦

C

k dimensionless form parameter k = 1.0339 ·

Ry

Rx

2

_/

π

L length of contact along the y axis, m

m

1 i

slope of the straight line (P

_i−1

P

_i+1

)

m

_{2 i}

slope of the line carried by the vector − → u

resulting i

m

_{2 i}

=

_m⁻¹

3 i

m

_{3 i}

slope of the straight line (OP

_i

) N rotational speed, rps

p pressure distribution, Pa p = p

₀

· q 1 −

^y_b²2

p

₀

maximum Hertzian pressure, Pa p = p

₀

· q 1 −

^y_b2²

P specific load, Pa

R

_{p i}

distance from the cam rotation axis O to the point P

_i

, m

Rq

_i

r.m.s roughness of the contacting surfaces, µm

R

_x

effective radius in the rolling di- rection x, m

1 Rx

=

_r¹

x1

+

_r¹

x2

R

_y

effective radius in the orthogonal direction y, m

1 Ry

=

_r¹

y 1

+

_r¹

y 2

r

x,y

radii of curvature of cam (1) and roller (2), in the rolling and or- thogonal directions, m

S slip between the two surfaces S =

^u¹_u^−u²

1

U dimensionless speed parameter U =

_E^η0⁰·R^·ux

u entraining velocity in the rolling direction, m/s

u =

¹₂

(u

₁

+ u

₂

)

∆u sliding velocity between the two surfaces, m/s

∆u = |u

₁

− u

₂

|

u

_i

surface velocity of the two sur- faces, m/s

u

_{cam i}

camshaft rotational speed at the point P

_i

, m/s

u

_{cam i}

= u

resulting i

· cos θ

_i

u

resulting i

cam resulting speed at the point P

_i

, m/s

u

resulting i

= R

_p_i

· ω

_cam

u

_{roller i}

roller tangential speed at the point P

_i

, m/s

u

_{roller i}

= u

_{cam i}

· (1 − S)

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W dimensionless load parameter W =

_E0^w·R²_x

y follower displacement, m y

•

follower velocity, m/s

••

y follower acceleration, m/s

²

•••

y follower jerk, m/s

³

α pressure-viscosity coefficient at operating temperature, P a

⁻¹

β temperature-viscosity coefficient,

1/

^◦

C

δ total deformation of the contact- ing bodies, µm

δ =

_R^b²

x

η dynamic viscosity, P a · s

η

₀

oil dynamic viscosity at p = 0 and operating temperature, P a · s λ specific film thickness

λ = √

^h^min

Rq²₁+Rq²₂

µ coefficient of friction ν kinematic viscosity, m

²

/s

ν =

^η_ρ

ν

_i

Poisson’s ratio of the material i ω

_cam

camshaft rotational speed ρ fluid density, kg/m

³

ρ(x) radius of curvature of a profile, m ρ(x) = (

^1+f⁰^(x)²

)

^3/2

|f⁰⁰(x)|

σ composite surface roughness of the surfaces, µm

σ = pR

_q²₁

+ R

_q²₂

τ shear stress, Pa

τ = η

^∂u_∂y

θ

_i

angle formed between − → u

resulting i

and − → u

_{cam i}

, deg

u

cam i

= u

resulting i

· cos θ

i

∂u

∂y

velocity gradient, or strain rate,

s

⁻¹

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List of Figures

1.1 Map of Sweden - Location of Halmstad . . . . 12

1.2 Halmstad university buildings . . . . 13

2.1 The development of governmental regulations for NOx and particle emissions 16 2.2 Energy and mechanical losses distribution in an internal combustion engine 16 2.3 Volvo D12 truck Diesel engine with parts of the valvetrain mechanism en- larged . . . . 17

2.4 Illustration of the valvetrain mechanism . . . . 18

3.1 Main elements of the tribological contact . . . . 20

3.2 Representation of the numerical contact when a stable layer of third body is obtained . . . . 21

3.3 Solid rubbing on a plan : creation of a frictional force F . . . . 22

3.4 Main forms of damages . . . . 22

3.5 Laminar shear of fluid between 2 plates . . . . 24

3.6 The Stribeck diagram identifying the regimes of lubrication as convention- ally associated with specific lubricated engine components . . . . 25

3.7 Contacts where a lubricating film separates the surfaces in relative motion 26 4.1 2D model-geometry of a deformed EHL-contact . . . . 28

4.2 Contact is made of a central region where thickness h

₀

is constant, and a horseshoe-shaped constriction of minimum thickness h

_min

. . . . 29

4.3 Schematic illustration of the theoretical EHL model used in this work . . . 32

4.4 Cam profile and its distinct regions . . . . 33

4.5 Radius of curvature of a profile . . . . 34

4.6 Calculated radius of curvature, plotted in polar coordinate . . . . 35

4.7 Calculated radius of curvature, plotted in Cartesian coordinate . . . . 35

4.8 Geometry of two loaded cylinders rotating around their fixed centre . . . . 36

4.9 8 periods moving averaged slip measurements, and roller acceleration curve 37 4.10 Schematic representation of the tangential and resulting speeds at the point P

_i

. . . . 38

4.11 Resulting and tangential speeds of both cam and roller, subplotted with the entraining velocity u . . . . 39

4.12 Normal force on roller, at an engine speed of 1800 rpm and maximum injection force . . . . 40

4.13 8 measured points of the injection cam . . . . 40

4.14 Measured cam r.m.s roughness, subplotted with radius of curvature and jerk 41 4.15 Pressure distribution between two parallel cylinders . . . . 44

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4.16 Semi-length of contact b and maximum Hertzian pressure p

₀

as a function of cam angle . . . . 45 4.17 Thermal correction factor C

_T

values, subplotted with the entraining and

sliding velocities . . . . 46 4.18 Minimum and central film thicknesses, subplotted wih the specific film

thickness . . . . 47 4.19 Specific film thickness, subplotted with the ratio h0/hmin and the total

deformation . . . . 48 4.20 Photo of the test equipment, the top cover being removed . . . . 49 4.21 Comparison of specific film thickness of an unworn and a worn cam . . . . 50 4.22 Wear observations on the first injection cam . . . . 52 5.1 Control loop showing the interdependence between function, manufacturing

and characterization, the three essentials for producing complex surfaces . 53 A.1 Adhesive wear . . . . i A.2 Abrasive wear . . . . ii A.3 Surface fatigue . . . . ii A.4 Abrasion and reformation of a passive oxide film in a corrosive environment iii A.5 Mechanisms of fretting wear . . . . iii A.6 Principle of erosion . . . . iv A.7 Mechanisms of cavitation wear . . . . iv B.1 A Stribeck curve, showing the effects of Hersey number

^η·N_P

on friction

coefficient . . . . vi C.1 Follower motion curves, during one revolution of the camshaft at a constant

speed of 900 rpm . . . . ix

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Chapter 1 Work Environment

1.1 The city of Halmstad

1.2 The university of Halmstad

1.3 The Functional Surfaces Research Group 1.4 Volvo Powertrain

1.1 The city of Halmstad

Halmstad is located on the Swedish west coast, 150 km north of Malm¨ o and 150 km south of G¨ oteborg (see Fig. 1.1). Halmstad is a port, university, industrial center and summer resort. Manufactures include textiles, engineering, brewing, paper and shipbuilding is carried on.

The city itself has a population of 56 000 (2005) and is the seat of Halmstad Mu- nicipality, which includes the region around the city and has 89 000 inhabitants (2006), but there are always many more people around. Tourists, businessmen, members of the armed forces, and students make sure that entertainment and culture prosper all the year round.

Chartered in 1307, Halmstad was an important fortified city of Denmark before being conquered by Sweden in 1645. Halmstad celebrates its 700-year anniversary this year.

1.2 The university of Halmstad

The university of Halmstad is a medium sized university which recently celebrated its 20th anniversary as an independent institution of higher education with its own vice- chancellor. The first courses in tertiary education began in 1973.

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14 Chap. 1: Work Environment

Figure 1.1: Map of Sweden - Location of Halmstad

At present the university has some 40 degree programmes, 7000 students and 500 em- ployees, regrouped in 5 fields of education : Department of Humanities, Department of Teacher Education, School of Business and Engineering, School of Information Science, Computer and Electrical Engineering and School of Social and Health Sciences. Most of the study programmes lead to either a Bachelor’s or Master’s degree.

The university has also well-developed research environments, most with a unique national or international profile. Research at Halmstad university is made up of 27 pro- fessors, 16 readers and 91 research students.

1.3 The Functional Surfaces Research Group

I have performed my internship within the Functional Surfaces Research Group, leaded by Pr. Bengt-G¨ oran Ros´ en. The research in this group has the aim to produce surfaces 100% ”tailor-made” for specified purposes. Whether a dental implant will last 5 or 50 years or if our cars and trucks will be able to reduce their petrol consumption or if a mobile phone will have a high-quality texture appearance are topics addressed within the scope of the research group’s work.

The research has a wide application range. General methods within research areas,

such as signals analysis, statistics, physical metrology, and quantitative topography char-

acterisation can be applied to support engineering applications.

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1.4 Volvo Powertrain 15

Figure 1.2: Halmstad university buildings

The applications vary from the automotive industry with manufacturing of low fuel- consumption engines, silent gear boxes, and complex car body panels, to manufacturing of dental implant surfaces and characterisation of artificial hip joint-implants for improved function and long product life. Focus for the research is to analyse surface topography and texture to enable detailed modelling of manufacturing and function of general surface applications.

The two main application areas, Automotive and Biotech, are organized in project areas ; engine cylinder-liner and piston interactions, transmission surfaces as valvetrain components, car body panel surfaces, and dental implant surfaces. Common for the automotive applications is the endeavour towards friction and wear control.

1.4 Volvo Powertrain

I have carried out my final year project in collaboration with Volvo Powertrain, one of the world’s biggest manufacturer of heavy-duty 9-18 liters Diesel engines.

Volvo Powertrain is the Volvo Group Strategic Center for powertrain issues. The scope covers complete powertrain systems, components such as engines, transmissions and driven axles.

Volvo Powertrain has operations in Sweden, France and North and South America.

The Business Unit incorporates powertrain development and manufacturing activities

representing approximately 8 500 employees around the world.

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Chapter 2 Aim of the project

2.1 Background 2.2 Purpose

2.3 Description of the valvetrain mechanism

2.1 Background

Customer demands and governmental regulations drive product development. What cus- tomers want today are cars and trucks that are more reliable, cost effective, environmen- tally friendly, safer, comfortable and silent. Some of these demands are directly related to tribology of engine components and mechanical systems with lower friction and wear will operate with less power loss and will last longer. Governments, in turn, are imposing ever-stricter regulations requiring better fuel economy and lower emissions. Fig. 2.1 [Die]

shows the governmental emissions regulations for the European truck industry in coming years. These demands will mean that mechanical components will have to be able to withstand higher loads, operate with less energy loss, and be able to function with longer service intervals.

Fig. 2.2(a) shows in the broadest sense the manner in which the energy of the fuel is distributed. About 60% of the energy is dissipated in the form of heat, either from the engine surfaces or down the exhaust pipe. Mechanical actions may account for a further frictional loss of the order of 15%, leaving only a quarter of the original energy in terms of brake power [Tay98].

In a similar way, Fig. 2.2(b) describes the breakdown of the mechanical losses in the engine with the piston assembly being responsible for almost one-half of friction losses.

It can be noted that losses associated with the valvetrain can be 10% or more of the mechanical losses [Tay98]. But it is clear that the energy distribution and mechanical loss distribution will vary with engine type and operating conditions.

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18 Chap. 2: Aim of the project

Figure 2.1: The development of governmental regulations for NOx and particle emissions

Tribological improvements which consist in lowering friction and improving wear re- sistance in engines will play a major role in future developments. Several solutions are available to reduce friction and improve the wear resistance of surfaces. Examples are improvements in lubrication, better design from a tribological point of view (roughness, contact mechanics, surface coatings) and surface hardening to improve material properties.

(a) Fuel energy distribution (b) Mechanical losses distribution

Figure 2.2: Energy and mechanical losses distribution in an internal combustion engine

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2.2 Purpose 19

2.2 Purpose

Cams are used in internal combustion engines to provide a specific prescribed motion to a valvetrain system. The components studied here are valvetrain machine elements for heavy-duty Diesel engines. Design of the Volvo D12 overhead camshaft valve train mechanism can be seen in Fig. 2.3 ; it will be described in the next subsection. The injection cam is one of the most problematic parts of the camshaft : while exhaust and intake valves are exerting a moderated pressure on cams, injection cams are subjected to high pressures from the fuel injector. High pressures are needed for spraying small drops of fuel which allow a better combustion in the chamber. Therefore, friction and wear are constant problems encountered in camshaft development.

Figure 2.3: Volvo D12 truck Diesel engine with parts of the valvetrain mechanism enlarged

Design of camshafts from a tribological point of view has been improved significantly in the last 20 years, but to this day, extensive problems still persist for many manufacturers.

In order to improve durability and efficiency, attention is now drawn on the following tribological design challenges to take up in the coming years for the automotive cam and follower [Tay98] :

• Improving surface profile, surface roughness and mixed lubrication considerations.

• Development of a linkage between lubrication mechanics and chemical mechanics, with a better understanding of the role of additives in reaction films.

• Consolidation of development and understanding of lubricant rheology to make more effective design predictions.

• Wear modelling linking to failure, materials, lubrication and thermal considerations.

• Satisfactory provision of lubricant.

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20 Chap. 2: Aim of the project The satisfactory lubrication of the cam and follower contact in internal combustion en- gines has proved to be the most difficult of all the tribological components. The primary function of the lubricant is to separate contacting surfaces, thus preventing metal-to- metal contact and premature cam failure. In cam operation, elastohydrodynamic lubri- cation films are generated which reduce interaction of the contacting surfaces. For these tribomechanical elements, numerous methods have been developed to calculate the thick- ness of these films.

The purpose of this work is to investigate the behavior of the oil film in the cam and roller contact, in order to predict regimes of lubrication and thus to identify the probable wear zones of the injection cam. Confrontation with experimental results will also be done. Future work to achieve is to discover the influence of the different parameters on oil film thickness, by performing a multivariate analysis. The next step will focus on mod- elling the wear of injection cams, and finally establishing quantified correlations between wear and oil film thickness.

The outline of this report is structured as follows :

• Chapter 3 gives basic notions of tribology, friction, wear and lubrication, and de- scribes accurately the different regimes of lubrication,

• Chapter 4 is focused on the tribological study of the cam-roller contact, i.e the evaluation of oil film thickness from elastohydrodynamic film theory,

• Chapter 5 is about the prospects to investigate in the framework of my MSc work.

2.3 Description of the valvetrain mechanism

The camshaft’s function in an engine is to open and close the valves. Its design results in valves being opened and closed at a controlled rate of speed as well as at a precise time in relation to piston position. The Volvo D12 valvetrain mechanism is composed of a rocker arm with a roller follower, used to open and shut the intake and exhaust valves and also to pump up the pressure in the Diesel injector placed between the intake and exhaust rocker arms (see Fig. 2.4).

Figure 2.4: Illustration of the valvetrain mechanism

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Chapter 3 Introduction to tribology : friction, wear & lubrication

3.1 Tribology

3.1.1 The tribological contact 3.1.2 The concept of third body 3.2 Friction

3.3 Wear

3.4 Lubrication 3.4.1 Viscosity

3.4.2 Regimes of lubrication

3.4.3 Conformal and non-conformal surfaces

3.1 Tribology

Tribology is the science of interacting surfaces in relative motion and the word originates from the Greek word ”tribos” which means ”rubbing”. The science includes sub-areas such as friction, wear and lubrication.

Friction is the resistance to bodies moving against each other and is always present when bodies are in motion. Friction can either be dry or viscous and in the former case we make a distinction between static and dynamic friction ; and in the latter case friction develops due to molecular forces between adjacent fluid layers.

Wear is a destructive process where surface material is removed from one or both of the two bodies in relative motion.

Finally, lubrication is a way of controlling both friction and wear. Lubricants can be either solid or fluid type, and their main purpose is to reduce the friction and protect the surfaces against wear. The work presented in this report deals with fluid film lubrication.

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22 Chap. 3: Introduction to tribology : friction, wear & lubrication

3.1.1 The tribological contact

The tribological contact is composed of four main elements (see Fig. 3.1 [CK00]) :

• solids A and B correspond to bodies in contact,

• the environment E,

• the interfacial environment I, also defined as third body (lubricant, wear particles).

Figure 3.1: Main elements of the tribological contact

Contact implies the notion of normal load applied on the solids, which generates me- chanical stresses (whose amplitudes depend on bodies geometric and topographic charac- teristics). The relative movement between two bodies has several consequences :

i). a resistance in displacement (due to the coefficient of friction), which leads to tan- gential stresses,

ii). a dissipation of energy (in form of heat) which drives to a heating of surfaces. High temperatures can modify mechanical properties of materials (elastic and plastic deformations),

iii). phenomena of solids separation (the lift) by the third body.

3.1.2 The concept of third body

In the 1970s, Godet proposed the concept of the third body in order to unify the problems

of friction and wear in dry contacts with the theory of lubrication. In the case of a bear-

ing, the fluid at the interface supports the load, separates the materials in contact and

accommodates the sliding speed. Even without an interfacial fluid, Godet [God84] showed

that, in many applications, a medium at the interface still exists and is constituted by

detached particles from the materials or by pollutant elements from outside the contact

(see Fig. 3.2 [FIB06]).

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3.2 Friction 23

Figure 3.2: Representation of the numerical contact when a stable layer of third body is obtained

3.2 Friction

The force known as friction may be defined as the resistance encountered by one body in moving over another. It is always exerted in the direction opposite to the movement (for kinetic friction) or the potential movement (for static friction) between two surfaces in contact. It is not a fundamental force, as it is made up of electromagnetic forces between atoms (interfacial connections, adhesive force). When contacting surfaces move relatively to each other, the friction between the two objects converts kinetic energy into thermal energy (heat).

Static friction occurs when the two bodies are not moving relatively to each other. It corresponds to the initial force to get an object moving. Rolling friction is classified under static friction, because there is no relative velocity at the contact.

Kinetic (or dynamic) friction occurs when two bodies are moving relative to each other and rub together. It corresponds to the force necessary to keep the motion at constant speed (ex : sliding friction, fluid friction).

According to the Coulomb model, the coefficient of friction is a dimensionless scalar value which describes the ratio between the frictional force F and the normal load P (see Fig. 3.3) :

µ = F

P (3.1)

where µ is the coefficient of friction, P is the normal force exerted between the surfaces (here : P = body weight) and F is the tangential force exerted by friction.

In the laws of sliding friction, the frictional force is proportional to the normal load,

and is independent from the apparent area and sliding velocity. In rolling contact, the

frictional force inversely proportional to the radius of the rolling element and is lower for

smoother surfaces.

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24 Chap. 3: Introduction to tribology : friction, wear & lubrication

Figure 3.3: Solid rubbing on a plan : creation of a frictional force F

3.3 Wear

Wear is a consequence of friction. It is a process in which interaction of surfaces of a solid with the working environment results in the dimensional and functional loss of the solid, with or without loss of material (see Fig. 3.4 [KC00]).

Considering a tribological approach based on the nature of phenomena at the origin of the damages, we can distinguish 5 main wear processes

¹

:

• adhesive wear,

• abrasive wear,

• surface fatigue,

• corrosive wear (+ fretting),

• erosion / cavitation.

These five processes of wear can be found in an engine group. The valvetrain compo- nents are mainly affected by adhesive wear and surface fatigue.

Figure 3.4: Main forms of damages

1The 5 wear processes are detailed in Appendix A.

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3.4 Lubrication 25

3.4 Lubrication

Fluid film lubrication occurs when opposing bearings surfaces are completely separated by a lubricant film. A lubricant is any substance that reduces friction and wear and provides smooth running and a satisfactory life for machine elements. Lubricants also allow to transfer heat, carry away contaminants and debris, transmit power, and prevent corrosion.

Most lubricants are liquids (such as mineral oils, synthetic esters, silicone fluids), but they may be solids (such as PTFE) for use in dry bearings (ex : aeronautic), greases for use in rolling-element bearings, or gases (such as air) for use in gas bearings [Ham94].

Typically, lubricants contain 90% base oil (most often petroleum fractions, called mineral oils) and less than 10% additives (such as antioxidants, corrosion and rust inhibitors, anti-foaming...).

The physical and chemical interactions between the lubricant and the lubricating sur- faces must be understood in order to provide the machine elements with satisfactory life.

First, we shall give a definition of the most important property of an oil for lubricating purposes : its viscosity. Then, the four lubrication regimes will be described, followed by a brief discussion about conformal and non-conformal surfaces.

3.4.1 Viscosity

The friction between surfaces which are completely separated (no asperity contact) is due only to the internal friction of the liquid, namely, its viscosity. The viscosity of a fluid may be associated with its resistance to flow ; it is a measure of the resistance of a fluid to deform under shear stress [Ham94].

i). The dynamic viscosity η expresses the relationship between the shear stress τ and the velocity gradient

^∂u_∂y

.

τ = η ∂u

∂y (3.2)

ii). The kinematic viscosity ν characterises the ratio of the viscous force to the inertial force (function of the fluid density ρ) :

ν = η

ρ (3.3)

Fluids which flow like water, obeying to the linear relation between shear stress τ and strain rate

^∂u_∂y

, are called Newtonian fluids. According to Newton’s postulate, oil molecules were visualized as small balls that roll along in layers between flat planes. Since the oil will ”wet” and cling to the two surfaces, the bottommost layer will not move at all, the uppermost layer will move with the velocity of the upper plane, and the layer in between will move with a velocity directly proportional to the distance between the two planes.

This type of orderly movement in parallel layers is known as ”streamline”, ”laminar”,

”viscous” or ”Couette” flow [Ham94], see Fig. 3.5.

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26 Chap. 3: Introduction to tribology : friction, wear & lubrication

Figure 3.5: Laminar shear of fluid between 2 plates

3.4.2 Regimes of lubrication

A useful concept for the understanding of the role of different regimes of lubrication is the Stribeck curve as shown in Fig. 3.6 [Ham94]. It is a plot of two non-dimensional groupings : the coefficient of friction µ on the ordinate and a variation of the Hersey number

^{2 η·N}_P

as abscissa (sometimes referred to as the Sommerfeld grouping) ; where η is the dynamic viscosity (Pa.s), N is the rotational speed (rps), P is the specific load (Pa).

With the development of the understanding of regimes of lubrication, this plot has increasingly incorporated the film thickness ratio λ on the abscissa as shown in Fig. 3.6, the modified Stribeck diagram [PT98]. The film thickness ratio has proved to be a valuable design concept, since it has led to an appreciation of the occurrence of surface interaction in a range of lubricated machine elements, and a recognition that surface topography can have a highly significant role in the performance and durability of such components. λ is defined as the ratio of the film thickness to the composite surface roughness, as follows :

λ = h

_min

pRq

₁²

+ Rq

₂²

(3.4)

where :

λ is the dimensionless film thickness ratio (or specific film thickness), h

_min

is the minimum film thickness (µm),

Rq

_i

are the r.m.s roughness

³

values of the two surfaces in contact (µm).

Values of the film thickness ratio are used to differentiate the different regimes of lubrication (see Fig. 3.6). Four regimes of lubrication are identified [PT98] :

• Hydrodynamic, in which the surfaces are completely separated by a film of lubri- cant, and the generation of pressures in the film to carry the load is achieved by

2A precise description of the effects of Hersey number on friction coefficient is given in Appendix B

3The r.m.s roughness is defined as the root-mean-square deviation of the profile from the mean line :

Rq²= 1 L

Z L O

y²(x) · dx

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3.4 Lubrication 27 hydrodynamic action, in which the dynamic viscosity of the lubricant is the prime lubricant characteristic. In this regime, friction is generated by shearing of the oil.

• Elastohydrodynamic, in which the surfaces are also in theory separated, but the contact is much more concentrated, the films are thinner and other physical phenomena (elastic distortion of the surfaces and the effect of pressure on dynamic viscosity) are influential. The work presented in this report deals exclusively with contacts that operate in this regime.

• Mixed, in which a lubricated contact experiences some degree of asperity contact between surfaces and the overall behavioral characteristics and load capacity are defined by both (elasto)hydrodynamic and boundary (see below) influences. Load is supported both by the oil film (via the phenomenon of hydrodynamic lift) and the contacts between surface asperities.

• Boundary, in which the surfaces are in normal contact with behavior characterized by the chemical (and physical) actions of thin films of molecular proportions. In the most severe conditions (low speed, critical viscosity, high loads), metal-to-metal contacts lead to a fast deterioration of surfaces.

Figure 3.6: The Stribeck diagram identifying the regimes of lubrication as conventionally associated with specific lubricated engine components

The regimes of lubrication conventionally associated with the piston rings, cam-follower

and engine bearings of an automobile are shown in Fig. 3.6. These components rely upon

different modes of lubrication for satisfactory performance and indeed each may encounter

more than one form of lubrication during a cycle. This reflects the challenges that face the

designer in improving operational characteristics, in response to legal and other pressures

on emissions control and energy efficiency.

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28 Chap. 3: Introduction to tribology : friction, wear & lubrication

3.4.3 Conformal and non-conformal surfaces

Conformal surfaces fit thightly into each other with a high degree of geometrical con- formity, so that the load is carried over a relatively large area. The load-carrying surface area remains essentially constant while the load is increased. Fluid film journal bearings (see Fig. 3.7(a)) and slider bearings have conformal surfaces. Hydrodynamic lubrication is commonly attributed to conformal surfaces ; the bearing pressure is generated in the high viscosity fluid due to the motion of the surfaces and the geometrical converging wedge created by the inclination of the surfaces. The film thickness is usually larger than 1 µm and the pressure rarely exceeds 10 MPa. Further, the pressure is normally not high enough to deform the surfaces elastically [Alm04].

Non-conformal surfaces do not geometrically conform to each other well and have small lubrication areas (nominally line or point contact), see Fig. 3.7(b). The lubrication area enlarges with increasing load but is still small in comparison with the lubrication area of conformal surfaces. Typical components that operate in this region are the contact between gear teeth, between a cam and its follower, or between a ball and its track in a ball bearing. The local pressures in the contact zone will generally be much higher than those encountered in hydrodynamic lubrication ; they typically range up to several GPa for steel components. The lubricating fluid film is normally less than 1 µm. Under these conditions, elastic deformation of the solid surfaces plays an important role, as does the pressure-viscosity effects of the lubricant. Lubrication in these circumstances is known as elastohydrodynamic [Hut92].

(a) Conformal contact (b) Non-conformal contact

Figure 3.7: Contacts where a lubricating film separates the surfaces in relative motion

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Chapter 4 Analysis of oil film behavior in the cam-roller contact

4.1 Physical explanation of EHL-contact

4.2 EHL film thickness model for elliptical contacts

4.3 Evolution of the parameters over one revolution of the camshaft 4.3.1 Radius of curvature of the cam

4.3.2 Entraining velocity

4.3.3 Normal load at the contact 4.3.4 r.m.s roughness of the cam 4.3.5 Constant parameters

4.4 Thermal correction of film thickness 4.4.1 Thermal correction factor

4.4.2 Maximum Hertzian pressure

4.4.3 Thermal correction values - Discussion 4.5 Numerical results

4.6 Confrontation with experimental results 4.6.1 Cam follower test equipment

4.6.2 Specific film thickness results

4.6.3 Observation of worn cams - Discussion

Lubrication is of significant importance in the prevention of cams from tribological processes and wear which cause failure. Many tribomechanical systems such as cams have contacting surfaces that do not conform to each other very well. The full magnitude of the load must then be carried by a very small contact area. The lubrication of the contacting surfaces of cams involves a complex technology. Contact loads on the contacting surfaces

29

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30 Chap. 4: Analysis of oil film behavior in the cam-roller contact of these tribomechanical systems tend to deform the material in the contact zone. Even if the loads are high, there is usually a thin film of lubricant between the contacting surfaces, so called an elastohydrodynamic film (EHL). The behavior of such films is complicated because their formation depends on mutually dependent factors : tribological properties of the lubricant and deformation of the contact zone.

4.1 Physical explanation of EHL-contact

In order to explain the physics in an EHL-contact, a simplified geometry is shown in Fig. 4.1. The geometry is 2D and is only the central part of the geometry shown in Fig. 3.7(b). The fluid film interacts with the moving surfaces through adhesive forces between surfaces and the adjacent fluid layers ; i.e. the fluid adheres to the surfaces.

Two main forces are created in the fluid film with a highly viscous fluid, the viscous and pressure forces. The movement between the fluid layers creates viscous forces and these are balanced by pressure forces [Alm04].

Figure 4.1: 2D model-geometry of a deformed EHL-contact

At the inlet of the EHL-contact, a geometrical wedge is formed by the converging surfaces. The fluid is dragged into the converging wedge due to the viscous forces, and in order to enforce mass conservation some of the fluid has to be pushed back by the pressure forces.

The pressure in the fluid is increased during the passage through the inlet region, as well as the pressure-dependent variables, such as viscosity and density. At some stage the pressure is high enough to deform the surfaces elastically. When this occurs, the geomet- rical converging wedge disappears and the fluid is transported through the central region of the contact. The oil film thickness in this region is called central film thickness h

₀

. A feature of EHL-contacts is that the central region has an almost constant film thickness, apart from a small curvature due to compressibility effects.

Another interesting feature of EHL-contacts is the characteristic pressure peak occur-

ing close to the exit region, see Fig. 4.1. In this region, the pressure will drop rapidly

due to the diverging surfaces where the fluid cavitates. The decrease in pressure results

in smaller elastic deformations and a constriction of the surfaces close to the outlet. The

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4.2 EHL film thickness model for elliptical contacts 31 same effect applies once again ; i.e a geometrical wedge is created at the outlet. A part of the fluid is pushed back in order to enforce mass conservation, and a pressure peak is created at the position of the exit constriction, where the minimum film thickness h

_min

can be found.

Thus, formation of an EHL film is the combination of three main effects : (1) formation of an hydrodynamic film (due to the pressure generated by the oil wedge mechanism), (2) elastic deformation of the two surfaces, and (3) increase of oil viscosity with respect to pressure (piezoviscosity effect, also called pressure-viscosity index).

4.2 EHL film thickness model for elliptical contacts

According to experimental results of literature ([Ham94], [Geo00]), high loaded EHL- contacts are assumed to be elliptical, as shown in Fig. 4.2.

(a) EHL-contact shape visualized by optical interferometry

(b) Schematic illustration of EHL-contact

Figure 4.2: Contact is made of a central region where thickness h

₀

is constant, and a horseshoe- shaped constriction of minimum thickness h

_min

In the 1970s, Hamrock and Dowson [HD76] [BD81] published a series of articles giving a numerical analysis of the elastohydrodynamic lubrication. Several equations have been independently derived by various investigations for predicting EHL minimum and central film thicknesses.

Theoretical investigation of EHL involves solving Reynolds equation

¹

while taking account of the variation of lubricant viscosity with pressure, and allowing for the elastic

1The differential equation governing the pressure distribution in fluid film lubrication is known as the

”Reynolds equation” (Reynolds, 1886). For time-invariant conditions while neglecting side leakage for EHL, the appropriate Reynolds equation is :

d dx

ρ · h³ η

dp dx

= 12 · ud (ρ · h) dx

The Reynolds equation is derived in two different ways, from the Navier-Stokes and continuity equations, and directly from the principle of mass conservation.

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32 Chap. 4: Analysis of oil film behavior in the cam-roller contact distortion of the bounding surfaces caused by the hydrodynamically generated pressure distribution.

Assumptions of the model are the following : isothermal flow, newtonian, piezoviscous and incompressible lubricant, fully flooded lubrication, hard elastic materials. Thirty-four cases were used to generate the minimum film thickness h

_min

and central film thickness h

₀

formulas for EHL elliptical conjunctions :

h

_min

= 3.63 · R

_x

· U

^0.68

· G

^0.49

· W

^−0.073

· 1 − e

^−0.68·k

(4.1)

h

0

= 2.69 · R

x

· U

^0.67

· G

^0.53

· W

^−0.067

· 1 − 0.61 · e

^−0.73·k

(4.2)

where U , G, W and k are dimensionless groupings defined as follows : U is the dimensionless speed parameter :

U = η

₀

· u

E

⁰

· R

_x

(4.3)

G is the dimensionless material parameter :

G = α · E

⁰

(4.4)

W is the dimensionless load parameter :

W = w

E

⁰

· R

²_x

(4.5)

k is the dimensionless form parameter (ellipticity parameter) :

k = 1.0339 · R

_y

R

_x

2/π

(4.6)

The variables used in this EHL model for elliptical conjunctions are : R

_x

effective radius in the rolling direction x, m

1 R

_x

= 1

r

_x1

+ 1

r

_x2

(4.7)

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4.2 EHL film thickness model for elliptical contacts 33 R

_y

effective radius in the orthogonal direction y, m

1 R

_y

= 1

r

_{y 1}

+ 1

r

_{y 2}

(4.8)

r

_x,y

radii of curvature of cam (1) and roller (2), in the rolling and orthogonal directions, m E

⁰

effective modulus of elasticity, Pa

E

⁰

= 2 · 1 − ν

₁²

E

₁

+ 1 − ν

₂²

E

₂

⁻¹

(4.9)

E

_i

modulus of elasticity of the material i, Pa ν

i

Poisson’s ratio of the material i

u entraining velocity in the rolling direction, m/s

u = 1

2 (u

1

+ u

2

) (4.10)

u

i

surface velocity of the cam and roller follower, m/s

η

₀

oil dynamic viscosity at p = 0 and operating temperature, Pa.s

α pressure-viscosity coefficient at operating temperature, P a

⁻¹

, such as :

η (p) = η (p

₀

) · e

^α·(p−p⁰⁾

(4.11)

w normal load at the contact, N

The minimum oil film thickness, together with the surface roughness, determines when full fluid film lubrication begins to break down. The expression of the specific film thick- ness λ introduced in Section 3.4.2 is reminded below :

λ = h

_min

σ = h

_min

pR

_q²₁

+ R

q2 2

(4.12)

where σ = pR

_q²₁

+ R

q2

2

is the composite surface roughness of the surfaces (also called

roughness standard deviation). The specific film thickness λ is used to describe the range

of values for the lubrication regimes ; its value provides a measure of how likely, and how

severe, asperity interactions will be in lubricated sliding [Hut92] :

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34 Chap. 4: Analysis of oil film behavior in the cam-roller contact

• for λ > 3, a full fluid film separates the two surfaces, asperity contact is negligible and both friction and wear should be low. However, many non-conformal contacts in machine components operate with λ < 3.

• the regime 1 < λ < 3 is termed partial EHL, or mixed EHL ; under these conditions some contact between asperities occurs.

• at λ = 1, the film thickness is of the same size as the contacting asperities. This is often considered to be the border between the boundary lubricated regime and the mixed lubricated regime.

• for λ < 1, no real lubricant film can develop and there is significant asperity contact, resulting in high friction. At extremely high loads or low sliding speeds, increasingly surface severe damage can occur on sliding (adhesive wear), and the behavior of the system depends critically on the properties of boundary lubricants, if present.

A schematic picture of the theoretical model used is given in Fig. 4.3.

Figure 4.3: Schematic illustration of the theoretical EHL model used in this work

The minimum and central film thicknesses developed above are not only useful for design purposes but also provides convenient means of assessing the influence of vari- ous parameters on the EHL film thickness. According to literature [Ham94], comparison between theoretical and experimental film thicknesses show a quite good accuracy of pre- dicted film thicknesses, between 10% and 20% of accuracy.

The next paragraph will focus on the evolution of the parameters of the model during

one revolution of the camshaft. Then, numerical results will be discussed, and adjustments

will be made to the model, in order to take into account thermal effects on the value of

oil film thickness.

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4.3 Evolution of the parameters over one revolution of the camshaft 35

4.3 Evolution of the parameters over one revolution of the camshaft

While some parameters of the model can be assumed to be constant during one revolution of the camshaft (discussed in Section 4.3.5), many parameters are variable and must be calculated as a function of cam angle :

i). the radius of curvature of the cam r

_x₁

in the rolling direction is a function of the cam profile,

ii). the entraining velocity u depends both on cam and roller peripheral speeds,

iii). the normal load at the contact w is directly linked to the injection pressure, which is a function of cam angle.

iv). measurements of r.m.s roughnesses on a brand-new machined camshaft have shown that R

_q

is dependent on the cam angle.

4.3.1 Radius of curvature of the cam

The notion of radius of curvature is directly linked to the cam profile

²

, which is obtained with the principle of ”inversion” : the cam is considered as the fixed member and the follower is then moved to its proper position (same relative motion). The cam profile is thus the enveloppe of the follower profile as the follower is positionned around the cam.

Volvo D12 injection cam profile and its distinct regions are shown in Fig. 4.4.

Figure 4.4: Cam profile and its distinct regions

The shape of a curve at any point depends on the rate of change of direction called curvature. We can construct for each point of the curve a tangent circle whose curvature

2Cam profile also provides crucial information – for design considerations – about follower motion characteristics ; see Appendix C.

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36 Chap. 4: Analysis of oil film behavior in the cam-roller contact is those of the curve at that point. The radius of the circle is called radius of curvature.

Fig. 4.5 shows the centre C of the radius of curvature of a point p of the curve. If the cam profile is in Cartesian coordinate form y = f (x), the expression of the radius of curvature is given by Eq. 4.13 [Rot03]. Fig. 4.6 and 4.7 respectively show the calculated radius of curvature plotted in polar coordinate, and in Cartesian coordinate.

ρ(x) = (1 + f

⁰

(x)

²

)

^3/2

|f

⁰⁰

(x)| (4.13)

Figure 4.5: Radius of curvature of a profile

We can notice that the radius of curvature is continuously changing as we move toward other points of the curve. Overall, values of radius of curvature follow the cam profile curve, and the four different regions can be clearly identified :

i). the cam nose has a small radius of curvature of approximately 22 mm between 15 and 30 cam-degrees,

ii). the circular shape radius decreases linearly from 51.5 to 36.5 mm, between 40 and 270 cam-degrees,

iii). the cam ramp is characterized by a quasi-linear rise then decrease of the radius of curvature between 270 and 329 cam-degrees, reaching a local maximum value of 46 mm at 295 cam-degrees,

iv). the flank can be assimilated as the ”quasi-plain” area of the cam, between 329 and 345 cam-degrees. It is important to note that numerically, the radius of curvature of a plain surface tends toward infinity. It explains the presence of vertical asymptotes and high absolute values of the radius of curvature in this region. Moreover, the flank presents a slight concave curvature (while the whole cam profile presents convex surfaces), which leads to negative values of the radius. The end of the flank is characterized by an arc of circle which acts as a transition between the ”quasi-plain”

area of the flank and the nose (intervals 345-360 and 0-13 cam-degrees).

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4.3 Evolution of the parameters over one revolution of the camshaft 37

Figure 4.6: Calculated radius of curvature, plotted in polar coordinate

Figure 4.7: Calculated radius of curvature, plotted in Cartesian coordinate

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38 Chap. 4: Analysis of oil film behavior in the cam-roller contact

4.3.2 Entraining velocity

a/ Slip measurement

Velocities of both cam and roller can be easily visualized as the contact between two cylinders or discs rotating at the appropriate speeds to give the correct combination of rolling and sliding contact. Fig. 4.8 shows two cylinders 1 and 2 of radii R

₁

and R

₂

rotating around their fixed centres in opposite directions and in the presence of a viscous fluid. Their peripheral speeds through the line of contact are u

₁

and u

₂

respectively. In this case, u

₂

> u

₁

, but the directions of both are such as to draw the viscous fluid into the gap between them, thus the entraining velocity u, which must be incorporated into the film thickness model, is given by [Wil05] :

u = 1

2 (u

₁

+ u

₂

) (4.14)

This is also known as the rolling velocity. In our example, because u

1

does not equal u

₂

there is also an element of relative sliding velocity between the two surfaces. This sliding velocity is equal to :

∆u = |u

1

− u

2

| (4.15)

The slip is defined as the relative difference between cam and roller velocities, as follows :

S = u

₁

− u

₂

u

₁

= u

_cam

− u

_roller

u

_cam

(4.16)

Figure 4.8: Geometry of two loaded cylinders rotating around their fixed centre

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4.3 Evolution of the parameters over one revolution of the camshaft 39 A method for slip analysis between the camshaft and the roller of a Volvo D12 engine was developed at Finnveden Powertrain AB, using high-speed camera [Mal06]. Slip was measured for an engine speed of 1800 rpm (i.e. camshaft speed of 900 rpm) at the maximal injection force. Moving averaged results are plotted in Fig. 4.9, and compared with acceleration.

Figure 4.9: 8 periods moving averaged slip measurements, and roller acceleration curve

By observing simultaneously the two curves, it can be noticed that the slip curve follows interesting trends. When the acceleration keeps constant values, the slip oscil- lates around zero. But when acceleration varies suddenly, peaks can be observed quasi- instantaneously in the slip curve. This is particularly obvious between 330 and 345 cam- degrees, where roller acceleration rises suddenly. This leads to a negative value of the slip, down to -0.13 (meaning that roller speed is 1.13 times higher than cam speed). The effect of roller decceleration on slip between 15 and 40 cam-degrees is less marked. Moreover, two areas where slip is subjected to strong variations remain difficult to explain, 60 to 90 cam-degrees, and 230-270 cam-degrees. Thus, it seems evident that the phenomenon of slip also depends on other parameters.

b/ Calculation of velocities

In order to obtain the entraining velocity u, it is necessary : i). first, to calculate the cam tangential speed u

_cam

,

ii). then, to find out the roller tangential speed u

roller

using the expression of slip.

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40 Chap. 4: Analysis of oil film behavior in the cam-roller contact For a camshaft speed of ω

_cam

= 900 rpm, and knowing the cam profile curve, cam tangential speed can be calculated as follows (see Fig. 4.10) :

u

cam i

= u

resulting i

· cos θ

i

(4.17)

where :

u

resulting i

is the cam resulting speed at the point P

_i

, m/s

u

resulting i

= R

_p_i

· ω

_cam

(4.18)

R

_{p i}

is the distance from the cam rotation axis O to the point P

_i

, m θ

_i

is the angle formed between − → u

resulting i

and − → u

_{cam i}

, deg, defined as :

tan θ

_i

= m

_{2 i}

− m

_{1 i}

1 + m

_{1 i}

· m

_{2 i}

(4.19)

m

1 i

is the slope of the straight line (P

i−1

P

i+1

), assumed to be parallel to − → u

cam i

m

_{2 i}

is the slope of the line carried by the vector − → u

resulting i

m

_{2 i}

= −1 m

3 i

(4.20)

m

_{3 i}

is the slope of the straight line (OP

_i

)

Figure 4.10: Schematic representation of the tangential and resulting speeds at the point P

i

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4.3 Evolution of the parameters over one revolution of the camshaft 41 The roller tangential speed can now be found out using Eq. 4.16 rewrited as follows :

u

_{roller i}

= u

_{cam i}

· (1 − S) (4.21)

Finally, the entraining velocity u is calculated using Eq. 4.14. Velocities curves are plotted in Fig. 4.11.

Figure 4.11: Resulting and tangential speeds of both cam and roller, subplotted with the entraining velocity u

4.3.3 Normal load at the contact

The normal force w acting on the roller follower is directly calculated from the fuel in- jector pressure. Values of normal load on roller at an engine speed of 1 800 rpm and for the maximum injection force (approximately 12 kN ) were provided by Volvo Powertrain.

They are plotted in Fig. 4.12, layered with the radius of curvature of the injection cam.

The fuel injection takes place during 35 cam-degrees, between the end of the cam

flank and the lobe of the nose. The maximum force on roller reaches 20 000 N . A residual

force of 1 500 N is still present during the rest of the camshaft revolution, due to inertial,

frictional and spring forces.

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42 Chap. 4: Analysis of oil film behavior in the cam-roller contact

Figure 4.12: Normal force on roller, at an engine speed of 1800 rpm and maximum injection force

4.3.4 r.m.s roughness of the cam

Root-mean-square roughnesses R

_q

of a brand-new machined camshaft were mesured

³

for 8 different angles of the injection cam, as shown in Fig. 4.13. Values of r.m.s roughnesses, averaged on three measurements, are displayed in Fig. 4.14, the curve being interpolated linearly between the eight measured points, so as to have an order of magnitude.

Figure 4.13: 8 measured points of the injection cam

The significance of cam profile accuracy is emphasized. A surface may appear smooth

3A Surfascan profilometer was used for the measurements, using a stylus of 2 µm, considering a length of measure of L = 19 mm (assumed to be the length of contact between the cam and the roller).

TRIBOLOGICAL ANALYSIS OF INJECTION CAMS LUBRICATION