Xin Q. Diesel Engine System Design

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720 Diesel engine system design

between the cam and the at-faced follower is counter-formal (unlike the

conformal contact in the engine bearings), the contact pressure is much higher

and the oil lm thickness is much lower than that in the engine bearings.

In boundary lubrication, the friction is affected by the solid materials and

lubricant additives which are related to the reaction lm formed on the

contact surface asperities. The properties of the bulk lubricant are of minor

importance and the coefcient of friction is essentially independent of oil

viscosity, load, speed, and apparent area of contact. The friction coefcient

depends on the nature of the boundary lubricant, which may become less

effective at higher temperatures. The boundary lubrication friction force

is proportional to the load. High wear occurs in boundary lubrication. In

the mixed lubrication regime, the cam–follower contact characteristics are

determined by a combination of thin-lm and boundary lubrication effects.

In this regime, the physical properties of the bulk lubricant and the chemical

properties of the boundary lubricant are all important. High oil lm thickness

may reduce friction. Higher engine speed promotes the elastohydrodynamic

lubrication and weakens boundary lubrication at the cam–follower interface so

that the overall friction coefcient reduces when the engine speed increases,

as veried by Teodorescu et al. (2002). Their measurement showed that

for a pushrod valvetrain with a at-faced follower in a four-stroke diesel

engine, the coefcient of friction at the cam–follower interface (including

the follower–bore friction) decreases linearly from 0.11 at 700 rpm engine

speed to 0.073 at 1700 rpm.

The valvetrain component loading and velocity exhibit strong instantaneous

varying characteristics within an engine cycle. For example, at the cam–

follower interface, the load at low speeds is mainly the valve spring force

which peaks at the cam nose, while the load at high speeds is dominated by

the dynamic inertia force which may vibrate violently from valve opening

to closing. The contact sliding velocity also has its own unique kinematic

characteristics. All these factors affect the lubricating oil lm thickness and

the lubrication regime with a strong instantaneously varying characteristic,

and affect the cycle-average value of the friction force. Teodorescu et al.

(2002) provided the experimental data for the instantaneous friction force

of each major component of a pushrod valvetrain in a diesel engine.

The relative proportions of the contribution from each component to

the overall valvetrain friction are dependent on designs. For example, the

contribution from the cam–follower friction can be dominant for a direct acting

OHC with a at-faced follower. The contribution from its large camshaft

bearing is also important. In this case, the overall valvetrain friction force at

low speeds is dominated by the mixed/boundary lubrication characteristics of

the cam–follower interface. The overall valvetrain friction force at high speeds

may be largely inuenced by the hydrodynamic lubrication characteristics

of the camshaft bearings. On the other hand, if a roller follower is used for

a valvetrain, the mixed/boundary lubrication characteristics of the overall

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721Friction and lubrication in diesel engine system design

valvetrain are less visible because the rolling friction contributes much less

to the overall friction.

When the valvetrain friction characteristics are assessed against design

or operating parameters, all the above factors need to be considered and

the conclusion depends on the particular situations for the given valvetrain.

In general, the following trends for the overall valvetrain friction can be

concluded.

∑ The cam–follower friction force tends to decrease with engine speed.

The hydrodynamic friction of other valvetrain components increases with

engine speed. The friction of the seals basically stays constant. Because

the cam–follower friction usually dominates, the overall valvetrain friction

force often decreases with increasing engine speed.

∑ At low speeds, the proportion of cam–follower friction is greater in

the overall valvetrain friction, and it is more difcult to maintain the

elastohydrodynamic lubrication than at high speeds.

∑ For the mixed/boundary lubrication dominated valvetrains (e.g., at-faced

follower), the friction torque decreases as the engine speed increases.

∑ For the fully developed hydrodynamic lubrication oil lm, the friction

force is not sensitive to load change. For the less or marginally

developed hydrodynamic lubrication oil lm, a load increase may break

the lm and bring the regime to the mixed lubrication oil and result

in a friction increase due to asperity contact. For the mixed/boundary

lubrication, a load increase can increase the friction. Therefore, in the

boundary–friction–dominated valvetrains or operating conditions (e.g.,

the at-faced follower, low speeds, high temperatures), the valvetrain

friction is more load-sensitive. In this case, a reduction in valve spring

load or inertia load may have a great benet. The effect of the load from

the hydraulic lash adjuster on camshaft bearing friction is usually very

small. The lash adjuster load acting on the cam base circle comes from

the internal oil pressure acting on the plunger and an additional return

spring load of the plunger.

∑ A lower oil temperature gives higher viscosity and higher viscous shear

friction in the bearings and the valve guides. On the other hand, a lower

oil temperature may thicken the oil lm via the increased viscosity. It

promotes good boundary lubricant protection for the friction modier

additives and reduces the boundary friction via less severe surface

asperity contact. For the boundary/mixed friction dominated valvetrains,

lower oil temperatures reduce friction. The effects of oil temperature

and viscosity were investigated by Choi et al. (1995) for a valvetrain

and certain engine bearings.

∑ For mechanical lash adjusters, the valvetrain lash may affect valvetrain

friction to a certain extent via the duration of the valve event loading

cycle.

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722 Diesel engine system design

The following design measures may reduce valvetrain friction:

∑ Each valvetrain conguration has its unique friction distribution and

characteristics among its components. The design solution needs to be

properly tailored. For example, a direct acting OHC does not have a

rocker arm and is very stiff. It may use the lowest weight and spring

force, but its camshaft bearings may be large due to the lack of a rocker.

For this conguration, reducing its bearing friction can be effective.

∑ Four general guidelines are: (1) reducing the sliding motion to minimize

the friction at the mixed/boundary interfaces (e.g., using a rolling contact

to replace a sliding contact); (2) promoting an oil lm formation at the

cam–follower interface (e.g., reducing spring or inertia load, increasing

oil entraining velocity, promoting lubricant availability, and preventing

oil starvation via direct spray rather than oil splash); (3) using friction

modier additives in lubricant oils; and (4) reducing surface roughness

of the contact.

∑ Using a roller follower and reducing valve spring preload or spring rate are

the two most effective solutions to reduce valvetrain friction, especially at

low speeds. However, it should be noted that the roller design increases

the Hertzian contact stress signicantly and probably requires a camshaft

material change (e.g., using steel camshaft). Moreover, a softer valve

spring may reduce the valvetrain separation speed unless the speed can

be recovered by a lighter valvetrain mass or higher stiffness.

∑ Using a rolling contact may signicantly reduce the friction at the rocker

arm fulcrum.

∑ Camshaft bearing friction can be reduced by reducing the bearing diameter

and length and optimizing the bearing clearance.

∑ Friction modied oils can signicantly reduce valvetrain friction, even

for the roller followers. Oil viscosity has only a minor inuence on the

boundary friction dominated valvetrains.

Valvetrain friction measurements and comparisons have been conducted by

Armstrong and Buuck (1981) and Kovach et al. (1982).

10.7.3 Valvetrain lubrication and friction analysis process

In valvetrain lubrication and friction analysis, the valvetrain kinematic and

dynamic analysis data and Hertzian stresses are used as input. The isothermal

elastohydrodynamic lubrication theory (line or elliptic contact models) along

with an assumed lubricant viscosity are used to predict the lubricating oil lm

thickness and the elastohydrodynamic friction force. The mixed lubrication

model may be included at various levels of complexity to estimate the boundary

friction caused by surface asperities. The average surface temperature can be

calculated after the friction force is known. The lubricant temperature can be

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723Friction and lubrication in diesel engine system design

assumed to be equal to the average surface temperature of the cam across the

contact area. Then the lubricant viscosity can be adjusted according to the

lubricant temperature, and the whole calculation process may iterate until the

results are convergent. Moreover, there are two special considerations to be

accounted for in the friction calculations: (1) the effect of follower (tappet)

rotation for the at-faced follower; (2) the effect of roller slippage for the

roller follower. Follower rotation and roller slippage are two important topics

in diesel engine system design.

The valvetrain lubrication and friction analysis procedures have

been described by a number of researchers. The valvetrain friction was

broken down to model each component individually. In the analytical and

experimental work by Staron and Willermet (1983) and Crane and Meyer

(1990), the cam–follower friction force was calculated on an instantaneous

basis by using the elastohydrodynamic theory, and the friction forces of

other components were calculated on a cycle-average basis. Paranjpe and

Gecim (1992) also took an instantaneous-friction calculation approach and

compared ve different valvetrain congurations (i.e., direct acting overhead

cam, pushrod, end-pivoted nger follower, center-pivoted nger follower,

and cam-in-head) with simulation. In their comparison, they made different

valvetrains equivalent by maintaining the same valve lift, the same valvetrain

no-follow speed, and the same input parameters with only a few exceptions.

They found that the direct acting OHC valvetrain had the lowest friction.

The two-nger follower valvetrains had the highest friction. The cam-in-head

valvetrain stayed in between the previous two.

10.7.4 Cam–follower friction analysis for the ﬂat-faced

follower

The lubrication and oil lm thickness conditions at the cam–follower interface

are vital to wear and durability for the valvetrain. The friction at that interface

is important at low speeds, but usually not at high speeds, for three reasons.

First, at high speeds the cam load at the cam nose deceases because the spring

force is offset by the dynamic inertia force of the valvetrain (although the

cam load at the cam ank increases). Secondly, high speeds promote the

hydrodynamic lubrication at the cam–follower interface to reduce friction.

Thirdly, at high speeds the hydrodynamic friction forces of other valvetrain

components (e.g., the camshaft bearings, the valve guides) increase and

may have a larger contribution than the cam–follower interface. This may

be the case when the cam–follower friction is minimized by using a roller

follower. However, for at-faced followers the friction at the cam–follower

interface is usually dominant. A lot of emphasis has also been placed on the

lubrication analysis of the cam–follower interface in the valvetrain friction

area for the reasons of wear, scufng, pitting, and polishing. Earlier valvetrain

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724 Diesel engine system design

friction research was conducted by Naylor (1967) and Dyson (1977, 1980).

Valvetrain lubrication and cam friction analysis was reviewed by Dowson

et al. (1986), Taylor (1991, 1993b, 1994), Zhu (1993), and Teodorescu et

al. (2003), including the analytical models and the experimental evidence

to support the models.

The  at-faced follower is widely used in direct acting OHC valvetrains (a

popular design option especially in light-duty applications) and some pushrod

valvetrains. The kinematic and lubrication analysis of cam and  at-faced

follower in a direct acting OHC valvetrain were provided by Taylor (1993b).

The contact loading and Hertzian stress at the cam–follower interface can

be determined by valvetrain dynamics calculations. Taylor (1993b) provided

a summary and references for the prediction of the oil  lm thickness at the

cam–follower interface by using the Reynolds equation under the assumption

of rigid counter-formal surfaces. In fact, Taylor (1993b) emphasized that

the elastohydrodynamic lubrication models pertaining to the surface elastic

deformation and the viscoelastic effect of the lubricant must be used for the

cam–follower contact to calculate the instantaneous minimum and central oil

 lm thickness (at the center of the nominal Hertzian contact). The pressure

distribution on the contact patch should satisfy both the Reynolds equation for

the oil  lm and the elasticity equations for the deformation of the contacting

bodies in the elastohydrodynamic lubrication. Dowson and Toyoda (1979)

provided the original modeling. The elastohydrodynamic simpli ed line-

contact formulae for smooth surfaces are cited here to illustrate the parametric

dependence:

central

HU =HU

HU 2HU

HU65HU

HU.HU

07..07

40-40

30.30

90..90

01.01

06..06

90..90

10.43

where H

is the dimensionless oil  lm thickness normalized by the radius of

curvature r

ROC

(i.e., h

o,min

= H

o,min

ROC

and 1/r

ROC

= 1/r

ROC1

+ 1/r

ROC2

), U

lub

is a dimensionless speed parameter proportional to the entraining velocity and

oil viscosity (U

lub

= m

v/(ϑ

ROC

), v = 0.5(v

+ v

)), G

lub

is a dimensionless

material parameter proportional to a pressure viscosity coef cient (G

lub

Cϑ

, where C is a pressure exponent), and W

lub

is a dimensionless normal

load parameter per unit length (W

lub

= F

/(ϑ

ROC

CAM

), where F

is load,

is elastic modulus of solids in contact, b

CAM

is the cam width). Note

that the oil  lm thickness is relatively insensitive to the load. A detailed

calculation example was provided in Appendix 2 of Taylor (1993b). For the

more sophisticated elliptic contact models the reader is referred to Staron

and Willermet (1983) and Yang et al. (1996) for applications. Dowson and

Higginson (1977) proposed a simpli ed empirical formula

o,central

= 16(m

ROC

)

0.5

10.44

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725Friction and lubrication in diesel engine system design

where h

o,central

is the central oil  lm thickness in microns, m

is the oil

viscosity at the contact zone entry condition, v is the oil entraining velocity,

ROC

is the combined radius of curvature of the cam and the follower, and

the speed–viscosity parameter m

v is in N/m.

Note that these calculations are based on quasi-static (steady state)

assumptions by ignoring the transient effects. The hydrodynamic lubrication

‘wedge’ effect is considered while the important dynamic ‘squeeze  lm’

effect is ignored. Smooth surfaces are also assumed in the calculation. More

sophisticated calculations of oil  lm thickness may consider the effects of

squeeze  lm (cited by Dowson et al., 1986; Scales et al., 1996), surface

topography and the elastic deformation of the surface asperities (Lee and

Patterson, 1995), and the non-Newtonian effect (Yang et al., 1996). In fact,

Lee and Patterson (1995) analyzed a roller follower and found that the

modi ed oil  lm thickness by considering the surface roughness effect did

not differ signi cantly from the result obtained by using the smooth-surface

assumption because the elastohydrodynamic  lm thickness is a weak function

of load.

The thickness-to-roughness ratio may be calculated subsequently to

assess the severity of the lubrication and the surface asperity contact. The

cam–follower interface is in the severe mixed lubrication regime. The friction

force is equal to the sum of the elastohydrodynamic friction force and the

boundary friction force due to surface asperity contacts,

f,CAM

= F

f,CAM,h

+ F

f,CAM,b

10.45

Mixed lubrication models at various levels of complexity may be used to

estimate the boundary friction. Staron and Willermet (1983) used the line

contact elastohydrodynamic theory, and they proposed a simple mixed

lubrication model as

bfribf

fCAMfC

fC,,fC

ri,ri

fC,,fC

AM,,AM

fCAMfC,,fCAMfC

Ff =Ff

(

Ff (Ff

F (F

(

Ff (Ff

(

bfribf

(

bfribf

(

F (F

(

ri,ri

(

ri,ri

)

– 11 –

<11 <

)

)11)

i11 i

f 11f

<11 <

0010

01 i01

01f 01

01 ≥01

10.46

where f

fri,b

is the boundary friction coef cient, F

is the cam load, and l is

the thickness-to-roughness ratio. Yang et al. (1996) used the more complex

elliptic contact elastohydrodynamic theory. They proposed a mixed lubrication

model by using the asperity contact theory of Greenwood and Tripp (1971)

and assumed the area of contact ellipse is the apparent area of asperity contact.

A similar mixed lubrication model was also discussed by Teodorescu et al.

(2003) and they used the line contact EHD theory and assumed the Hertzian

contact area is the apparent area of asperity contact.

Taylor (1993b) suggested using the central oil  lm thickness to calculate the

elastohydrodynamic shear friction force at the sliding contact as follows:

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726 Diesel engine system design

fCAMfC

central

fC,,fC

AM,,AM

fCAMfC,,fCAMfC

o,o

()

vv()vv

()

vv()vv

vv()vv – vv()vv

10.47

where b

is the half width of Hertzian contact area on the cam, and v

– v

the sliding velocity of the contact point between the cam and the follower.

An appropriate pressure-dependent lubricant viscosity must be used in

equation 10.43 because such a non-conformal contact is highly viscoelastic

(i.e., the viscosity increases exponentially under high oil pressure). Because

the elastohydrodynamic lubrication pressure distribution in the contact zone

is almost the same as the Hertzian pressure, the pressure used to calculate

viscosity can be taken from the calculated Hertzian pressure. In fact, the

non-Newtonian behavior of the lubricant affecting the shear rate also plays

a major role because the shear stress is lower than the Eyring strength here.

Yang et al. (1996) and Teodorescu et al. (2003) provided more complex

models of shear friction force by considering the non-Newtonian effect. The

calculated friction force renders the coef cient of friction to be calculated, and

it needs to be compared with a pre-determined limiting friction coef cient (e.g.,

0.08–0.12). If the calculated friction coef cient is greater than the limiting

value, the limiting value should be used. It should be noted that the EHD

oil  lm thickness could play a secondary role on the friction force compared

with the strong in uences of the rheological properties of the lubricant oil

and surface roughness for a very thin oil  lm (less than 0.1 micron).

The cam–follower friction power can be calculated by the following:



fCAMfC

CCAMCC

fC,,fC

AM,,AM

fCAMfC,,fCAMfC

fC,,fC

WF =WF

WF dWF

rN drN

WF dWF

fCAMfC

rN drN

CCAMCC

WF dWF

10.48

where r

is the perpendicular distance from the cam rotation center to the

friction force vector, and f

CAM

is the cam rotational angle. The temperature

rise at the cam–follower contact due to the frictional heat can be estimated

based on the  ash temperature concept proposed by Yang et al. (1996).

Figure 10.22 shows typical oil  lm thickness vs. cam angle (Soejima

et al., 1999). It should be noted that although it appears that the two spikes

of high oil  lm thickness occupy a short duration in time or cam angle scale,

they actually cover the majority of the cam  ank area all the way up to near

the cam nose if presented in a spatial view of the cam contour. This is due

to the large variation of the velocity of the point of contact across the cam

surface. Dowson et al. (1986) best illustrated this feature. In Fig. 10.22, it

is observed that the oil  lm thickness is small but constant in a small region

near the cam nose. It indicates a vulnerable lubrication condition in that region

compared to the thicker oil  lm in the majority of the cam  ank region. The

nearly constant  lm thickness around the cam nose is largely dominated by

the nearly constant cam radius of curvature and entraining velocity in that

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727Friction and lubrication in diesel engine system design

region. The two most vulnerable locations subject to the boundary lubrication

are the ones having theoretical zero oil lm thickness, which is predicted

by the quasi-static and ‘wedge effect only’ assumptions. The zero oil lm

thickness corresponds to zero mean entraining velocity due to the change in

direction of the lubricant entrainment. It should be noted that in reality the

oil lm thickness is not zero due to some ‘squeeze lm’ effect, as pointed

out by Taylor (1993b). At the cam ank region with large oil lm thickness,

the thickness-to-roughness ratio is usually much larger than 1 or 3, indicating

the elastohydrodynamic lubrication regime. Around the cam nose, a very

thin oil lm (in the order of 0.02–0.2 micron) may be maintained between

the cam and the follower, and the thickness-to-roughness ratio is usually

smaller than 0.5 or 1. This indicates the severe mixed lubrication regime

(including the elastohydrodynamic) or even the boundary lubrication. Note

that the criteria of thickness-to-roughness ratio used to judge the lubrication

regimes should vary accordingly when the oil lm thickness is predicted

with different types of models (i.e., with or without surface topography and

asperity deformation).

From equation 10.48, it is observed that the critical design parameters

in cam lubrication to achieve good (large) oil lm thickness are cam load

and the instantaneous mean entraining velocity. The instantaneous mean

entraining velocity is a function of the instantaneous radius of curvature

–180 –90 0 90 180

Cam angle, deg.

Oil:80N+MoDTP

1200 rpm

1000 rpm

Ls = 500N

k = 252N/mm

= 120 °C

1000 rpm

Friction force, N

Contact

load, N

Coefﬁcient

of friction

Min. oil ﬁlm

thickness, µm

200

100

2000

1000

0.12

0.08

0.04

0.00

0.4

0.2

0.0

10.22 Changes of contact load, friction force, friction coefﬁcient, and

minimum oil ﬁlm thickness with cam angle just before and after the

scufﬁng occurrence (from Soejima et al., 1999).

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728 Diesel engine system design

of the contact point, lateral sliding velocity, and cam rotational speed. The

cam load is affected by spring force, valvetrain mass, and engine speed.

The radius of curvature is affected by the cam base circle size and the cam

prole. High entraining velocity and large radius of curvature increase the

oil lm thickness. Taylor (1994) showed an example of a 2.0-liter engine

with an end-pivot follower valvetrain. When the base circle radius was

increased by 20%, the follower radius of curvature was increased by 12%,

the valve spring rate was reduced by 10%, the Hertzian stress at the cam

nose was reduced by 19%, the friction power was reduced by 3% and the

oil lm thickness at the cam nose was increased by 17%.

10.7.5 Flat-faced follower rotation

The effect of follower rotation (spin) of a at-faced follower (tappet) on wear

reduction has long been recognized. Offset design has been widely used to

promote follower rotation by offsetting the follower centerline from the cam

centerline (along the direction of the cam lobe width). Tapered cam prole

along the lobe width has been used to make the velocities between the two

mating surfaces more equal. With follower rotation, lubricant entrainment

is improved, and wear is constantly distributed over a larger contact surface

rather than a narrow patch. Therefore, durability is improved.

The effect of follower rotation on friction reduction was relatively new

to the design community, and it inspired great interest in exploring this

phenomenon by experimental and analytical means. Pieprzak et al. (1989),

Willermet and Pieprzak (1989), Willermet et al. (1990), Paranjpe and Gecim

(1992), Taylor (1994) and Cho et al. (2004) conducted experimental and

analytical investigations on follower rotation and its effect on cam friction.

As pointed out by Taylor (1994), in order to validate the predictive friction

models, it has been common to restrain the follower rotation to make the

kinematics in the experiment as precisely dened as in the theoretical

model. However, in practice the at-faced follower is free to rotate in order

to enhance durability. This difference causes the discrepancy between the

friction modeling result and the friction experimental test result in a real

engine. Follower rotation is also related to the slip at the friction interface.

Therefore, understanding, modeling, and designing the follower rotation to

achieve low valvetrain friction and wear is of practical importance, despite

the fact that the modeling of the dynamic friction torque driving the follower

rotation is very challenging.

Follower rotation is driven by the turning torque produced by the friction

force at the cam–follower interface acting at an offset distance from the

follower centerline. All design/contact geometry and other forces acting on

the follower affect the follower rotation, for example, the circumferential

viscous shear friction force between the follower and its bore, which is

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729Friction and lubrication in diesel engine system design

a damping force to resist the rotation. The driving torque determines the

follower’s rotational speed. The offset distance determines the linear speed

of the follower at the contact. In an extreme case, if the linear speed of the

follower is equal to the linear speed of the cam lobe, the contact will have

rolling friction without slip and the friction will be very low. The primary

reason for the effective friction reduction due to follower rotation is that

a partial rolling motion is induced between the contact surfaces, hence the

friction coefcient is reduced compared to the sliding motion.

The follower rotation exhibits interesting characteristics as listed below,

and some theoretical insights are provided here to explain the phenomena

observed from the measurements.

∑ The instantaneous follower rotational speed of the follower varies as a

function of cam angle. The speed gradually increases as the valve starts

to open more, and reaches a maximum value near the cam nose (i.e.,

when the valve is fully open), then gradually decreases as the valve

closes. On the cam base circle after the valve fully closes, the follower’s

rotational speed gradually decays before vanishing.

∑ At low engine speeds, the instantaneous follower’s rotational speed tends

to be symmetric around the cam nose. At high speeds, the pattern becomes

asymmetric with the peak rotational speed located often at the cam closing

side. The higher the engine speed, the more drift of the peak away from

the cam nose. When the engine speed increases, the peak value of the

rotational speed decreases, and it takes longer for the speed to decay to

zero extended on the cam base circle. For example, Taylor (1994) showed

that the peak rotational speed of the follower was 450 rpm at 549 rpm

camshaft speed; and the peak follower rotational speed decreased to 300

rpm at 2,052 rpm camshaft speed. As the engine speed increases, the

variation amplitude of the instantaneous rotational speed of the follower

becomes smaller, or in other words, the follower rotates more evenly.

∑ The cycle-average rotational speed of the follower tends to increase with

engine speed.

∑ The cycle-average rotational speed of the follower is substantially lower

than the camshaft rotational speed, for example, in the order of one-tenth

of the camshaft speed.

∑ Follower rotation is affected mainly by camshaft speed, the design of the

cam–follower contact geometry (e.g., size, eccentricity) and kinematics.

It is less affected by lubrication conditions.

∑ There was a correlation between the follower’s rotational speed and the

cam–follower friction torque within a cam cycle (Pieprzak et al., 1989;

Willermet and Pieprzak, 1989; Willermet et al., 1990). Faster follower

rotation results in lower friction torque. The effect is the greatest in the

region of the maximum valve lift where the rotational speed is high and

the contact becomes closer to rolling friction.

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