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Diesel-Xin-09.indd 650 5/5/11 11:59:19 AM

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651

10

Friction and lubrication in diesel engine

system design

Abstract: This chapter addresses engine friction and lubrication dynamics

modeling in diesel engine system design. It starts by introducing important

fundamental principles of engine tribology and builds up a three-level

system modeling approach of engine friction. The chapter summarizes

the friction characteristics and friction-reduction design measures for both

the overall engine system and individual subsystems such as the piston

assembly, the piston rings, the bearings, and the valvetrain.

Key words: engine tribology, friction, lubrication, cavitation, fuel economy,

piston assembly dynamics, piston ring, bearing, valvetrain, stiff ordinary

differential equation (ODE), numerical computation.

10.1 Objectives of engine friction analysis in system

design

10.1.1 Deﬁnition of engine friction

The friction work is dened as the total of mechanical (rubbing) friction

work and accessory work consumed. The rubbing friction is the work to

overcome the resistance to relative motion of all the moving parts of the

engine, including the piston assemblies, the bearings (for the crankshaft,

the connecting rod, the camshaft, the rocker arm, and the balance shaft,

if any), the front and rear oil seals and other bearing seals, the valvetrain,

the gears, the pulleys, the drive belts, and the chains. The accessories can

include part or all of the auxiliary devices driven by the engine, such as the

water pump, the oil pump, the fuel pump, the alternator (the generator), the

air pump or the EGR pump for emissions control, the air compressor for

the service brakes, the radiator cooling fan, the power-steering pump, and

the air conditioner.

Unlike the denition used by other authors which includes pumping work

as part of the total engine friction, the pumping work is not dened as part

of the friction work in this book for the following reasons:

∑ In four-stroke engines, the pumping work is dened as the work in the

exhaust and intake strokes. It is difcult to dene pumping work in

two-stroke engines due to the lack of these two pumping strokes.

∑ The pumping work can be either a positive quantity (i.e., a pumping

Diesel-Xin-10.indd 651 5/5/11 12:00:18 PM

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652 Diesel engine system design

‘gain’) or a negative quantity (i.e., a pumping ‘loss’). The pumping work

consists of two parts: the part due to engine delta P, and the part related

to engine volumetric efciency, as analyzed in the air system theory in

Chapter 4. The latter part is always a loss or dissipation work due to

the air ow restrictions through the valves and other restrictive orices/

ducts. However, the engine delta P can be either positive or negative,

depending on turbine area and turbocharger efciency. When the pumping

work is a positive gain, if it were included in the denition of the engine

friction work, the total engine friction could be completely offset to zero

or even a positive gain. This can be very misleading for comparing the

friction levels between different engines and for the design efforts of

reducing the engine mechanical friction.

∑ The pumping work is highly variable. Signicant differences can be seen

between the naturally aspirated engines and the turbocharged engines,

with large differences existing among the engines on the following

aspects: (1) turbine areas (e.g., in a VGT or wastegated turbine); (2)

turbocharger efciencies; (3) intake/exhaust restriction levels (related

to the intake/exhaust system design, the aftertreatment devices, or the

exhaust brake); and (4) engine operating conditions (speed, load, ambient

condition, etc.). If the pumping work were included in the denition of

engine friction, the friction work would become highly uncertain and

inconvenient for comparison.

∑ The pumping loss eventually dissipates in the form of exhaust heat

discharged to the ambient through turbulent mixing and non-isentropic

compression. The mechanical friction eventually dissipates in the form of

heat rejection to the cooling system. Their mechanisms are different.

∑ The theoretical background and the mechanisms are very different for

the pumping work and the mechanical (rubbing) friction. Modern engines

become increasingly complex, from turbocharger and EGR systems to

the exhaust brake. The pumping work belongs to the territory of the

air system theory, while the mechanical friction loss belongs to the

areas of lubrication and tribology. Their completely different academic

backgrounds make it necessary to separate the pumping work from the

scope of engine friction.

∑ Modern in-cylinder pressure measurement techniques and engine cycle

simulation software allow an accurate determination of the pumping work

so that there is no reason/need to mix it with the mechanical friction

work.

Engine motoring tests are often used to obtain engine friction data. It is

necessary to subtract the pumping work from the total motoring work in

order to obtain the ‘true friction work’ (i.e., the rubbing friction plus the

accessory work; Gish et al., 1958). The pumping work can be calculated by

using ÚpdV for the intake and exhaust strokes, where the cylinder pressure p

Diesel-Xin-10.indd 652 5/5/11 12:00:18 PM

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653Friction and lubrication in diesel engine system design

can be obtained from either engine testing or cycle simulation. Alternatively,

a less accurate but simpler approach can be used to estimate the pumping

loss, given as follows:

v

PM

EP

PMEPPM

exhaus

tm

pm

tmpmtm

p

pmppm

pp

intake

pp

intake

Cv

tm

Cv

tm

Cv

pm

Cv

pm

= (

pp = (pp

pp – pp

)

tm

)

tm

+

tm

+

tm

+

pm

+

pm

tm1tm

Cv

1

Cv

tm

Cv

tm1tm

Cv

tm

2

pm2pm

Cv

2

Cv

pm

Cv

pm2pm

Cv

pm

2

10.1

where C

1

and C

2

are the constants re ecting the valve  ow restrictions at

the intake and exhaust valves, respectively; v

mp

is the mean piston speed,

p

exhaust

is the exhaust manifold pressure, and p

intake

is the intake manifold

pressure.

It is important to clearly specify the auxiliary components included in the

accessory work. Usually, the oil, water, and fuel pump power are included,

but the power from the cooling fan, the alternator, the power steering pump

and other vehicle accessories may not be included in the engine motoring

friction power.

The above engine friction de nition can be expressed as follows:

ϖ

FMEP

= (ϖ

IMEP

+ ϖ

PMEP

) – ϖ

BMEP

10.2

ϖ

FMEP

= ϖ

MFMEP

+ ϖ

AFMEP

10.3

where ϖ

FMEP

is the friction mean effective pressure (de ned here as positive

value for convenience), ϖ

IMEP

is the indicated mean effective pressure, ϖ

PMEP

is the pumping mean effective pressure, and ϖ

BMEP

is the brake mean effective

pressure. The ϖ

MFMEP

and ϖ

AFMEP

represent the mean effective pressure

of the mechanical (rubbing) friction and the accessories, respectively. The

engine mechanical ef ciency is de ned by

h

v

vv

Em

ech

BM

EP

BMEPBM

BM

vv

BM

vv

EP

vv

EP

vv

BMEPBM

vv

BM

vv

EP

vv

BM

vv

FM

EP

FMEPFM

,

Em,Em

=

vv

+

vv

10.4

The rubbing friction power



W

f

W

f

W

and the friction force F

f

are related by



WF

v

ff

WF

ff

WF

WF =WF

WF

ff

WF =WF

ff

WF

10.5

where v is a characteristic velocity. Moreover, ϖ

MFMEP

is proportional to

engine design parameters according to the following relationship:

v

MF

ME

MFMEMF

P

MEPME

f

EE

f

EE

f

EE

W

f

W

f

NV

EE

NV

EE

Fv

f

Fv

f

NV

EE

NV

EE

Fv

f

Fv

f

Nn

EE

Nn

EE

BS

EE

BS

EE

=

NV

=

2

BS

2

BS

µ



10.6

More engine friction fundamentals are described by Heywood (1988).

10.1.2 The need to study friction in engine system design

Friction, as one of the engine performance attributes, directly affects fuel

economy, and is closely related to noise (e.g., piston slap and bearing impact)

Diesel-Xin-10.indd 653 5/5/11 12:00:19 PM

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654 Diesel engine system design

and wear (through the mixed and boundary lubrication). Internal combustion

engine friction has been constantly reduced over the past several decades,

nearly 10% per decade (Sandoval and Heywood, 2003). Among the total

mechanical losses in the diesel engine, the piston assembly may account

for 45–50%, bearings 20–30%, valvetrain 7–15%, and accessories 20–25%

(Taylor, 1993a). In order to completely address diesel engine system design

specications, engine friction needs to be researched by system engineers

for the following reasons:

∑ Engine friction modeling is important for the accuracy and effectiveness

of the engine system design tool – the cycle simulation model. Friction

affects the prediction of engine power, fuel economy, and heat rejection.

A reliable estimation of engine friction is also important for comparing

different design concepts related to conguration, component geometry,

and weight. The friction model needs to accurately reect the overall

engine friction at different operating conditions, and reect the parametric

dependency that a system engineer is concerned about (e.g., the impact

of engine bore, stroke, weight, and cylinder pressure).

∑ The system engineer is responsible for coordinating various performance

attributes such as fuel economy, noise, durability (e.g., wear), and cold

start capability. A thorough understanding of engine friction of each

related component is necessary.

∑ The system engineer is in charge of planning the fuel economy

improvement roadmap and friction reduction roadmap for the engine.

A good understanding of the contribution of each friction component

and their relative importance is necessary in order to decide the overall

system-level design strategy and coordinate the activities for component

engineers.

∑ Engine transient/controls simulation and fault diagnostics are important

topics in diesel engine system design. Mechanical friction prediction is

important for the torque-based controls at a system level. The friction

torque in the engine control unit is usually presented as a lookup table

with two input variables, the engine speed and the indicated torque. The

accuracy of the friction torque at steady-state and transient operations

is important for engine controls and advanced real-time diagnostic

functions. Friction models are also important for cold start analysis.

Not only is an accurate overall engine friction model needed, but an

instantaneous crank-angle-resolution friction model is also required in

order to accurately predict the engine speed uctuation. (The importance

of instantaneous friction model for fault diagnostics was mentioned by

Ciulli, 1993.)

Diesel-Xin-10.indd 654 5/5/11 12:00:19 PM

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655Friction and lubrication in diesel engine system design

10.1.3 The approach of engine system design to friction

The focus of engine friction research for the system engineer is different

from that for the component engineer. In component design, the most

sophisticated friction models are required. This may include the detailed

models for the piston assembly (the piston skirt and the rings), the valvetrain,

and the engine bearings. The topics of concern in component design usually

include the effect of design parameters on friction, lubrication, wear, motions,

blow-by, oil consumption, and noise. These requirements often require the

simulation model to possess high delity on hydrodynamic lubrication or

even thermo-elastohydrodynamic lubrication with advanced sub-models of

cavitation, lubricant viscosity, and surface roughness. These models tend to

be computationally expensive and highly specialized. At a system level, the

focus must be less detailed. Engine system design requires the system-level

engine friction model to possess the following three progressive levels of

complexity:

1. The level-1 engine friction model: This type of model focuses on the

overall engine friction mean effective pressure (FMEP) on a cycle-average

basis without the instantaneous (crank-angle-resolution) details of the

friction forces. The level-1 model lumps all different friction components

together and does not differentiate their lubrication regimes. However,

it does include a range of major design parameters such as engine bore,

stroke, bearing length, engine speed, and peak cylinder pressure.

2. The level-2 engine friction model: This type of model is more detailed

than the level-1 model, and focuses on the overall engine friction torque

on an instantaneous basis. It predicts the friction coefcients and the

friction forces for major components based on lubrication regime,

lubricant property and instantaneous loading of different components.

The level-2 model can be used in engine transient and fault diagnostic

simulations or for more detailed design parameter studies, while the

level-1 model ignores the instantaneous uctuations, underestimates

actual friction force around the ring TDC, and does not include so

many design parameters as inputs. Both the level-1 and level-2 models

need to be computationally fast and real-time capable.

3. The level-3 engine friction model: This type of model is the most complex.

With limited complexity, the level-3 model solves the lubrication Reynolds

equation analytically or numerically for lubricating oil lm thickness

and pressure distribution in a lubrication dynamics formulation. Then

the friction shear forces can be computed. This type of model is usually

not real-time capable and may have a broader range of applicability

extended for component designs by containing more fundamental physics

and more detailed parameters (e.g., surface topography). The level-3

model may be solved to generate the so-called Stribeck curves in order

Diesel-Xin-10.indd 655 5/5/11 12:00:19 PM



656 Diesel engine system design

to look up the coef cient of friction for the level-1 and level-2 models.

It can also help a system design engineer to thoroughly understand the

mechanisms involved in engine friction, lubrication, and wear.

10.2 Overview of engine tribology fundamentals

10.2.1 Friction fundamentals

In general, friction can be classi ed into static friction and dynamic friction.

Dynamic friction can be further divided into Coulomb’s friction and viscous

friction by different mechanisms. The static friction model is the classic

model of friction of Leonardo Da Vinci: friction force is proportional to

normal load, opposes the direction of motion, and is independent of contact

area. The break-away force necessary to initiate motion from rest in static

friction is often greater than the kinetic/dynamic (or Coulomb’s) friction

force. In Coulomb’s friction law, the friction force is only dependent on the

direction of velocity, not on the magnitude of the velocity. Moreover, the

Coulomb friction force is directly proportional to the applied normal load

and independent of the apparent area of contact. A typical example of the

Coulomb’s friction is the dry sliding or the boundary lubrication sliding

contacts between two metal pieces. The Coulomb friction force is calculated

by the following:

F

f,Coulomb

= f

fri

F

n

or

f

F

fr

f

fr

f

i

fC

F

fC

F

oulom

b

n

F

n

F

=

fC,fC

10.7

where f

fri

is the coef cient of friction and F

n

is the force applied in the normal

direction. Coulomb’s friction model, along with other fundamental friction

models commonly used in engineering, is shown in Fig. 10.1.

Viscous friction is another type of friction, caused by the viscosity of

the  uid. In viscous friction, the friction force is proportional to the sliding

velocity and goes to zero at zero velocity. The viscous friction force comes

from the shear stress in the  uid  ow. The ratio of the shear stress to the

velocity gradient is a measure of the viscosity of the  uid and is called the

coef cient of viscosity. These relationships can be expressed as follows, in

the case of the planar Couette  ow and based on Newton’s law of laminar

 ow viscosity:

FA

v

y

A

h

v

fv

FA

fv

FA

vc

y

vc

y

vc

A

vc

A

o

fv,fv

FA =FA

d

FA dFA

d

ydy

vc

d

vc

y

vc

ydy

vc

y

d

Ad A

vc

d

vc

A

vc

Ad A

vc

A

=

tm

m

ÚÚ

FA

ÚÚ

FA

ÚÚ

d

ÚÚ

d

FA dFA

ÚÚ

FA dFA

tm

ÚÚ

tm

FA

tm

FA

ÚÚ

FA

tm

FA

d

tm

d

ÚÚ

d

tm

d

FA dFA

tm

FA dFA

ÚÚ

FA dFA

tm

FA dFA

=

tm

=

ÚÚ

=

tm

=

Ê

tm

Ê

tm

Ë

tm

Ë

tm

Ê

tm

Ë

tm

Ê

tm

Ê

Á

Ê

tm

Ê

tm

Á

tm

Ê

tm

Ë

Á

Ë

tm

Ë

tm

Á

tm

Ë

tm

Ê

tm

Ë

tm

Ê

tm

Á

tm

Ê

tm

Ë

tm

Ê

tm

ˆ

¯

vc

¯

vc

ˆ

¯

ˆ

˜

ˆ

¯

˜

¯

vc

¯

vc

˜

vc

¯

vc

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

d ªd

Ê

Ë

Ê

Ë

Ê

Á

Ê

Ë

Á

Ë

Ê

Ë

Ê

Á

Ê

Ë

Ê

ˆ

¯

ˆ

¯

ˆ

˜

ˆ

¯

˜

¯

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

kv

v

kv

v

kv

10.8

where F

f,v

is the tangential viscous friction force, t is the shear stress, µ

v

is the dynamic viscosity of the  uid, v is the relative velocity, A

c

is the

contact area, h

o

is the  uid  lm thickness (such as the piston-to-bore or

Diesel-Xin-10.indd 656 5/5/11 12:00:19 PM



657Friction and lubrication in diesel engine system design

bearing clearance), k

v

is a dened viscous coefcient, and dv/dy is the

velocity gradient across the thickness of the oil lm (Fig. 10.1). Viscosity is

the primary factor resisting the motion in the laminar ow, such as in uid

lubrication. However, when the velocity increases to the level of turbulent

ow, the pressure differences resulting from the eddy currents rather than

the viscosity may provide the major resistance to the motion. The viscous

friction occurs in the hydrodynamic lubrication. It should be noted that unlike

Coulomb friction where the friction force is proportional to the normal load,

the viscous force may exist even at zero normal load (i.e., unloaded viscous

friction, for example sliding a rod within a lubricated clearance inside a

sleeve). Accordingly, there is no dened friction coefcient, per se, like that

in Coulomb friction. A typical example of the unloaded viscous friction is

the friction force on engine bearings at certain moments when the dynamic

loading becomes zero but the journal rotates at a constant speed. Another

example of unloaded viscous friction is the friction force on the piston skirt

near the middle of the intake or exhaust stroke where the piston side thrust

becomes zero but the piston velocity is high. When the dynamic loading is

greater than zero the viscous friction becomes loaded viscous friction. When

the velocity becomes zero (e.g., for piston skirt and piston rings at the TDC

Dynamic friction

force = f

fri

F

n

Viscous friction

force = k

v

Static friction force

Sliding velocity

(c) The static, Coulomb plus

viscous friction model

(d) The Coulomb, viscous

plus Stribeck friction model

Sliding velocity

Tangential viscous

friction force

Sliding velocity

Stationary surface

Moving surface at velocity v

(a) The Coulomb’s friction model (b) The viscous friction model

0

Friction force

Velocity

gradient

Surface

area

d

y

x

10.1 Commonly used fundamental friction models.

Diesel-Xin-10.indd 657 5/5/11 12:00:20 PM



658 Diesel engine system design

and the BDC), the viscous friction becomes zero. Figure 10.2 shows the

reaction force to the piston side thrust force, calculated viscous shear force

by using the two-dimensional Reynolds equation (to be detailed later) and the

calculated ‘coef cient of friction’ (de ned as the ratio of the shear friction

force to the normal side thrust). It is observed that at the moments where

the side thrust becomes zero, the coef cient of friction becomes extremely

large (or in nity) and hence very misleading. This shows that such a concept

of ‘friction coef cient’ should not be used to calculate the unloaded viscous

friction. It should be handled with great care when applied to the modeling

of the dynamically loaded viscous friction.

Both Coulomb friction and the viscous friction may exist at the same

time for an engine component, for example in the mixed lubrication regime.

Stribeck observed from the use of  uid lubrication in 1902 that the friction

force decreases continuously with increasing velocities at low velocities.

This phenomenon of a decreasing friction at increasing but relatively low

velocities is called the ‘Stribeck effect’ (Fig. 10.1).

In engine lubrication and friction, it is important to determine which friction

mechanism occurs and use the corresponding friction models appropriately.

Sometimes, in the case of loaded viscous friction, especially in the mixed

lubrication, the following forms of the de nition of the viscous friction

coef cient are seen in the literature:

Ff

Fv

f

F

Fv

fv

Ff

fv

Ff

fr

Ff

fr

Ff

in

Fv

in

Fv

fr

f

fr

f

i

fv

F

fv

F

n

Fv

n

Fv

fv,fv

Ff

fv

Ff

,

Ff

fv

Ff

fv,fv

Ff = Ff

or

Fv orFv

or or



10.9

Ff

F

fv

Ff

fv

Ff

fr

Ff

fr

Ff

in

Ff

in

Ff

fr

Ff

fr

Ff

i

fv

F

fv

F

n

F

n

F

fv,fv

Ff

fv

Ff

,

Ff

fv

Ff

fv,fv

Ff = Ff

Ff orFf

Ff Ff

Ff orFf Ff orFf



10.10

These forms of de nition were created in order to be close to or the same

as the form used in Coulomb friction because the Coulomb friction model

(equation 10.7) and the concept of friction coef cient are so widely used

due to their simplicity. These coef cients are often used as if the contacts

exhibit the Coulomb friction behavior although in reality they do not. These

de nitions of the friction coef cients for the viscous friction may be acceptable

for the constantly loaded components such as the piston rings, but they are

not always valid for the case of the dynamically unloaded viscous friction

such as for the piston skirt and the engine bearings. Andersson et al. (2007)

provide more details on various fundamental friction models.

10.2.2 Lubrication regimes and the Stribeck diagram

Different lubrication regimes have different friction mechanisms, and lead to

distinct friction and wear responses. Engine tribology modeling includes three

Diesel-Xin-10.indd 658 5/5/11 12:00:20 PM



10.2 Piston skirt dynamic normal load, viscous friction force, and calculated Coulomb-type ‘coefﬁcient of friction’.

Piston skirt load parameter

Total hydrodynamic lubrication friction

force acting on piston skirt thrust and

anti-thrust sides (N)

Lubricant force acting on piston skirt

in normal direction at thrust side and

piston pin bearing lateral force (N)

15000

10000

5000

0

–5000

–10000

0.0005

0.0004

0.0003

0.0002

0.0001

0

100

50

0

–50

–100

0 90 180 270 360 450 540 630 720

Crank angle (degree)

0 90 180 270 360 450 540 630 720

Crank angle (degree)

Radial clearance

20 micron

Radial clearance

30 micron

Radial clearance

40 micron

Radial clearance

20 micron

Radial clearance

30 micron

Radial clearance

40 micron

Radial clearance

20 microns

Radial clearance

30 microns

Radial clearance

40 microns

Radial clearance

20 microns

Radial clearance

30 microns

Radial clearance

40 microns

Calculated hydrodynamic lubrication

friction coefﬁcient for the piston skirt

0.1

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

This is the

problem of the

Coulomb-type

friction coefﬁcient

for dynamically

loaded

components

Diesel-Xin-10.indd 659 5/5/11 12:00:21 PM

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Xin Q. Diesel Engine System Design

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