Xin Q. Diesel Engine System Design

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690 Diesel engine system design

ovality in the circumferential direction. Usually, a piston skirt has a barrel

pro le at cold. At hot conditions the barrel shape and ovality change as the

piston expands thermally. As the piston moves laterally and tilts within the

clearance, the lubricating oil  lm thickness changes dynamically at each

moment during an engine cycle, and the oil  lm thickness distribution also

changes spatially on the piston skirt. The piston skirt wear durability can be

analytically characterized by the dynamic minimum oil  lm thickness within

an engine cycle at the thrust side and the anti-thrust side. When different

piston designs are compared, a larger minimum oil  lm thickness usually

re ects lower risk of wear and scuf ng.

The solution algorithm of the piston lubrication dynamics is brie y described

as follows. Denoting the location of the crank pin center as 1 and the piston

pin center as 2 in the piston-assembly dynamics model, the dynamics model

of the piston skirt can  nally be reduced to two second-order nonlinear

ordinary differential equations (ODEs) for the piston skirt tilting angle b

and the piston pin lateral displacement x

as follows (Xin, 1999):





(

)

(



=xf =

(xf (

(

xx,,xx

tx,,tx

,,,,,



)

10.26

Because of the nonlinear nature of the functions f

and f

in equation 10.26

(especially due to the lubrication force model), this ODE system cannot be

solved analytically. Time-marching numerical integration is necessary. The

accelerations



and



are calculated after the lubricant forces are calculated

by using the lubrication model 10.24 at every time step. The piston lateral

and tilting displacements and velocities must be solved by a time-marching

implicit integration. The primary motion of the piston assembly is calculated

based on the kinematic constraints between the components. The lateral and

vertical forces acting on the piston pin and the crank pin are calculated by

using the above-mentioned approach of force/moment balance.

10.4.4 Stiff ODE characteristics of lubrication dynamics

The stiff ODE feature is one of the most fundamental and important

characteristics in lubrication dynamics. The governing equations of any

lubrication dynamics problems are often stiff ordinary differential equations.

The stiff ODE features are generated from the Reynolds equation coupled

with the dynamics equations that include the acceleration terms (e.g., the

piston mass inertia or moment of inertia). The stiffness refers to the largest

eigenvalue l

ODE,max

of the Jacobian matrix of the ODE system for the piston

motion, equation 10.26, and to a stiffness ratio that is de ned as the ratio of

the largest eigenvalue to the smallest eigenvalue of the ODE system. The

stiffness affects the numerical stability of the time-marching integration. The

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691Friction and lubrication in diesel engine system design

stiffness is affected by the design and dynamic parameters. The following

parameters can make the l

ODE,max

and the stiffness ratio larger (i.e., more

stiff): smaller mass of the piston; smaller moment of inertia of the piston;

smaller skirt-to-bore clearance; longer length of the skirt; larger radius of

the skirt; higher oil viscosity; and larger dynamic eccentricity.

The high stiffness of the ODE system causes two types of numerical

instability, one for all time-marching explicit integration schemes, and the

other for some implicit integration schemes. The instabilities usually exhibit

large high-frequency oscillations in the lubricant force trace as a function of

time. These oscillations are numerical errors rather than true physical signals

(Fig. 10.10). The instabilities are related to the following: the stiffness of

the ODE system, the type of integration scheme (explicit or implicit), the

stability property of the implicit integration scheme, the time-step size,

and the deviation of the initial condition from the nal periodic convergent

solution. Explicit integration schemes usually cannot solve the stiff ODE

problems due to their extremely large numerical instabilities. The larger the

eigenvalue of the ODE, the smaller the time step that has to be used with the

explicit integrators in order to avoid the numerical instability. The time step

First cycle (µ

= 0.028 Pa.s)

First cycle (µ

= 0.028 Pa.s)

lub,th

(Radau IIA 2-stage)

lub,th

(Trapezoidal)

lub,th

(Gauss 2-stage)

lub,an

(Gauss 2-stage)

lub,an

(Radau IIA 2-stage)

lub,an

(Trapezoidal)

First cycle (µ

= 0.028 Pa.s)

First cycle (µ

= 0.028 Pa.s)

180 360 540 720

0 180 360 540 720

Lubricant forces (N)

Piston lateral velocity (m/s)

Piston clearance (mm)

Piston lateral velocity (m/s)

10000

8000

6000

4000

2000

–2000

–4000

–6000

0.03

0.02

0.01

–0.01

–0.02

–0.03

0.2

0.15

0.1

0.05

0.015

0.01

0.005

–0.005

–0.01

–0.015

–0.02

Corner 1 (Trapezoidal)

Corner 1 (Radau IIA 2-stage)

Corner 1 (Gauss 2-stage)

Corner 2 (Gauss 2-stage)

Corner 2 (Radau IIA 2-stage)

h2 (Radau IIA 2-stage)

h2 (Trapezoidal)

h1 (Trapezoidal)

h1 (Radau IIA 2-stage)

Corner 2 (Radau IIA

2-stage)

Corner 2 (Trapezoidal)

Crank angle (degree)

Crank angle (degree)Crank angle (degree)

10.10 Stiff ODE and numerical instabilities of implicit integration

methods with weak stability properties (1800 rpm, 70% load).

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692 Diesel engine system design

required is approximately the reciprocal of the largest eigenvalue. Lubrication

dynamics problems are generally highly stiff so that the time step which can

be used in the explicit integrators becomes impractically small. This results

in extremely long computing time and large accumulation of the round-off

errors during the course of the integration.

It should be noted that some implicit integration schemes with weak

stability properties (e.g., the Gauss or Lobatto IIIA type implicit Runge-Kutta

integration methods) also exhibit numerical instabilities during transient

simulations of the lubrication stiff ODE problems. The instability exhibits

in the lubricant force trace as oscillations (Fig. 10.10). Only the strongly

B-stable implicit integrators (e.g., the Radau IIA type implicit Runge-Kutta

methods) can compute both the lubricant force and the piston motions without

numerical instabilities. Moreover, the order of accuracy is also important for

time-marching integration. Higher stiff-order implicit integration schemes with

strong B-stability should be used to compute the dynamic response of such

stiff ODE systems. The stiff ODE features of piston lubrication dynamics

are summarized in Fig. 10.10. The stiff ODE characteristics of lubrication

dynamics have been extensively researched by Xin (1999).

10.4.5 Effect of piston design on skirt lubrication and

friction

Figure 10.11 shows the calculated piston side thrust within one engine cycle

at three speed and load conditions. It is observed that a longer connecting rod

reduces the piston side thrust. Figure 10.12 illustrates the computed lubricating

oil lm pressure distributions on the piston skirt. The oil pressure is generated

by a combination of lubrication ‘wedge’ and ‘squeeze lm’ effects caused by

the piston secondary motions. The zero pressures (i.e., equal to the ambient

gauge pressure) are caused by oil lm cavitation. Note that different piston

skirt proles may generate distinct patterns of the oil pressure distribution

on the thrust and anti-thrust sides. For example, during the expansion stroke,

a cylindrical skirt prole produces the oil pressure only at the thrust side,

while a barrel skirt prole generates the oil pressure at the lower portion of

the skirt on both the thrust and anti-thrust sides.

A comparison on the piston secondary motions between using the lubrication

model and ignoring lubrication in piston dynamics is provided in Fig. 10.13.

It shows the great difference in predicted piston lateral velocities.

The effects of the piston pin lateral offset and the vertical position of the

piston’s center of gravity are shown in Figs 10.14 and 10.15, respectively. It is

observed that they both have a great effect on piston skirt tilting or scraping.

The effect of lubricant oil viscosity is shown in Fig. 10.16. The piston skirt

hydrodynamic friction power increases with oil viscosity. Moreover, when

piston scraping occurs, the piston friction power increases signicantly due

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693Friction and lubrication in diesel engine system design

to the higher friction coefcient of the boundary lubrication in the surface

asperity contact during the scraping.

Moreover, simulation shows that as long as the piston skirt is designed

to operate within the hydrodynamic lubrication regime, at the same engine

speed but different loads, the piston skirt hydrodynamic lubrication friction

power varies only in a range of 0.2–2%, depending on the piston skirt

prole. However, different piston pin positions can result in a difference

of up to 10% in the hydrodynamic lubrication friction power of the piston

skirt. Higher friction corresponds to more violent secondary motions given

by the unfavorable piston pin position. Piston weight has a very small

inuence on piston skirt friction power. It also has a negligible effect on

the oil lm thickness. But piston weight reduction may decrease the kinetic

energy and the noise of piston slap in cold conditions. Simulation analysis

has revealed that an effective way to reduce piston skirt friction is to reduce

the skirt area (i.e., the skirt length or the lubricating wetted arc angle along

the circumferential direction of the piston). The reduction in skirt friction

power is basically linearly proportional to the reduction of the lubricated

skirt area. Figure 10.17 simulates the complex nature of the piston secondary

motions within the piston-to-bore clearance at a high engine speed. The

piston motions, the minimum oil lm thickness, and the skirt friction are

affected by piston design parameters.

Piston with shorter connecting rod at rated power

Piston with longer connecting rod at rated power

Crank angle (degree)

Piston pin lateral force (N)

10,000

5000

–5000

–10,000

–15,000

0 90 180 270 360 450 540 630 720

High speed, part load

Low speed, part load

10.11 Illustration of piston side thrust at different engine speeds and

loads.

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694 Diesel engine system design

Piston skirt with barrel-shape

axial proﬁle, thrust side, engine

condition: 1300 rpm 37 hp

Piston skirt with barrel-shape axial

proﬁle, anti-thrust side, 1300 rpm 37 hp

Piston skirt with cylindrical axial proﬁle,

thrust side, 2300 rpm 300 hp

Piston skirt with cylindrical axial proﬁle,

anti-thrust side, 2300 rpm 300 hp

Lubricating oil ﬁlm

pressure (MPa)

Skirt

bottom

Piston axial

direction

Crank angle

TDC

BDC

TDC

BDC

TDC

top

Expansion

stroke

Exhaust

stroke

Intake

stroke

Compression

stroke

10.12 Lubricating oil ﬁlm pressure distribution on piston skirt.

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695Friction and lubrication in diesel engine system design

h1 (Case 2)

(Case 2)

(Case 1)

h1 (Case 1)

h2 (Case 2)

(Case 2)

(Case 1)

Skirt-to-bore clearance (mm)

Piston lateral velocity (m/s)

Skirt-to-bore clearance (mm)

0.2

0.15

0.1

0.05

0.02

0.01

0.00

–0.01

–0.02

–0.03

–0.04

0.40

0.20

0.00

–0.20

–0.40

–0.60

–0.80

0.2

0.15

0.1

0.05

0 180 360 540 720

Crank angle (degree)

0 180 360 540 720

Crank angle (degree)

(a) Corner clearances of skirt

Corner 2 of skirt

Corner 1 of skirt

With lubrication

(Case 1)

Without lubrication

(Case 2)

Crank angle (degree) Crank angle (degree)

Corner 1 of skirt

0 180 360 540 720 0 180 360 540 720

(b) Corner lateral velocities

10.13 Illustration of piston secondary motions with and without skirt

lubrication at 1800 rpm 70% load.

Piston tilting angle b

(radian)

0.0005

0.0004

0.0003

0.0002

0.0001

–0.0001

–0.0002

–0.0003

–0.0004

–0.0005

Skirt tilting angles under different engine loads

and piston designs

100% load

Crank angle (degree)

Pin set 4 (e

= 0, e

= 2 mm)

Pin set 1 (e

= 0,

= –2 mm)

Pin set 3 (e

= 0, e

= 0)

Idling

180 360 540 720

30% load

100% load

75% load

50% load

Idling

10.14 Effect of piston pin lateral offset and engine load on piston

tilting at 1500 rpm.

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696 Diesel engine system design

10.5 Piston ring lubrication dynamics

10.5.1 Friction characteristics and piston ring design

Piston rings have the functions of sealing the cylinder gas to control blow-

by, transferring the heat, and controlling the oil consumption that are related

to smoke and particulate emissions. The blow-by refers to the escape of

the compression and combustion gases past the piston and the rings into

the crankcase, and is related to power loss and crankcase emissions. High

blow-by and high oil consumption often occur simultaneously. Sealing

is achieved by the gas forces acting on the top and the back of the rings

and also by the ring tension. Piston rings usually account for the largest

portion in mechanical friction and are subject to wear. Compared to the

compression rings, the oil ring usually has greater friction force due to its

higher tension and thinner thickness. A modern piston ring pack has usually

two compression rings and one oil-control ring. The top ring’s function is

primarily sealing the gas pressure. The oil ring’s function is oil control.

The function of the second ring is usually in between and more for oil

control. The compression rings may have various ring face proles (e.g.,

barrel – most common, plain, taper), different cross-sectional shapes (e.g.,

taper – most common for oil control to scrape the oil off the cylinder wall

during the downstrokes, keystone, rectangular, bevel step, bevel cut), and

different types of twist for sealing (i.e., no-twist, positive twist, negative

twist). As pointed out by Tian et al. (1996a, 1997), a positive static twist

can stabilize the ring when the land immediately above the ring has a higher

gas pressure, while a negative twist can generate ring utter if the gas force

and the axial inertia force are comparable in magnitude. For example, the

second compression ring may utter during the late part of the compression

stroke and the early part of the expansion stroke. The top compression ring

usually has a barrel prole. The second compression ring is commonly

0 180 360 540 720

Crank angle (degree)

0 180 360 540 720

Crank angle (degree)

h2 (L

CG,P

= 6.35 cm)

h1 (L

CG,P

= 6.35 cm)

h1 (L

CG,P

= 2.35 cm)

h3 (L

CG,P

= 2.35 cm)

h4 (L

CG,P

= 2.35 cm)

h3 (L

CG,P

= 6.35 cm)

h4 (L

CG,P

= 6.35 cm)

h2 (L

CG,P

= 2.35 cm)

Skirt-to-bore clearance (mm)

0.2

0.15

0.1

0.05

0.2

0.15

0.1

0.05

10.15 Effect of the vertical position of piston center of gravity on

piston secondary motions at 1800 rpm 70% load.

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Skirt-to-bore clearance (mm)

0.2

0.15

0.1

0.05

0.2

0.15

0.1

0.05

0 180 360 540 720

Crank angle (degree)

0 180 360 540 720

Crank angle (degrees)

0 180 360 540 720

Crank angle (degree)

Corner clearances of piston

= 0.028 Pa.s

= 0.014 Pa.s

= 0.007 Pa.s

Piston skirt power loss due

to friction (kW)

h1 (0.007 Pa.s)

h4 (0.007 Pa.s)

h3 (0.007 Pa.s)

h4 (0.014 Pa.s)

h3 (0.014 Pa.s)

h4 (0.028 Pa.s)

h3 (0.028 Pa.s)

h2 (0.007 Pa.s)

h1 (0.014 Pa.s)

h2 (0.014 Pa.s)

h1 (0.028 Pa.s)

h2 (0.028 Pa.s)

10.16 Effect of lubricant oil viscosity on piston secondary motions and skirt friction power at 1800 rpm 70% load.

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698 Diesel engine system design

designed to help control the oil by a scraping motion during the downstroke.

The piston rings may have different circumferential free shapes with distinct

characteristics of the tension force when they are placed inside the cylinder

bore. Some ring design takes advantage of the combustion chamber pressure

for sealing so that the ring tension can be reduced. The size of the end gap

affects blow-by, the gas pressure between the rings and ring dynamics. The

oil-control ring usually has two thin rails separated by a spring/expander.

The oil-control ring usually has the highest tension and contributes most to

the engine friction. All these design features, together with the piston skirt

motions and cylinder bore distortion, affect the lubrication dynamics and

the friction force of the ring. Effective lubrication has to be achieved with

minimum oil consumption, friction, and wear.

The piston rings develop hydrodynamic lubrication (with a friction

coefcient of 0.001–0.002) in the middle of the engine strokes and encounter

mixed to boundary lubrication (with a friction coefcient of 0.08–0.12)

as they approach the TDC and BDC. The ring–liner wear is usually most

severe immediately after the ring TDC, when the cylinder gas loading and

temperature are high and the ability to develop protective hydrodynamic

lubrication oil lm is hampered by low sliding speeds.

Piston ring tribology is a highly sophisticated and specialized area.

There are numerous publications and many review papers in this area. An

informative review on the historical development of piston ring technology

Most critical duration under

the risk of oil ﬁlm breakdown

1.5 mm piston pin lateral offset towards thrust side, long skirt,

high friction power

Zero piston pin offset, 18% shorter skirt length, friction

power reduced by 22%

0 90 180 270 360 450 540 630 720

Crank angle (degree)

Piston skirt oil ﬁlm thickness at thrust

side (micron or µm)

10.17 Effect of piston design (skirt length and piston pin offset) on

skirt friction power and oil ﬁlm thickness.

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699Friction and lubrication in diesel engine system design

can be found in Economou et al. (1979). Literature reviews on piston ring

tribology are provided by McGeehan (1978), Ting (1985), and Andersson

et al. (2002).

Excessively thick oil lm and high oil consumption cause particulate

emissions problems. The oil consumption via the piston rings is believed to be

the largest portion of total oil consumption in an engine, compared with other

sources such as the oil loss via the valve guides/seals, the oil leakage through

various seals (e.g., a turbocharger seal), and evaporative oil consumption

from the cylinder wall. The oil consumption via the rings is generated from

the throw-off of accumulated oil above the top ring, oil blow through the

top ring end into the combustion chamber, and the oil scraping by the edge

of the piston top land. The oil consumption rate due to piston ring pack and

blow-by usually increase with engine speed and load. Inter-ring pressure

control to stabilize the ring motions is important in reducing oil consumption.

The compression rings are often pushed against the upper side of the groove

during the intake stroke and stay on the lower side of the groove during other

strokes. The second compression ring often lifts up around the ring TDC.

The axial motion can easily become much more complex for a particular

design and engine operating condition. Piston ring axial motions and their

effect on oil consumption were studied experimentally by Furuhama et al.

(1979) and Curtis (1981). The oil consumption mechanisms were researched

by De Petris et al. (1996), Hitosugi et al. (1996), Thirouard et al. (1998),

and Herbst and Priebsch (2000). The effects of piston skirt lubrication on the

mechanism of oil supply to the oil ring and oil consumption were explored by

Ito et al. (2005) and Nakamura et al. (2005, 2006). The effects of piston ring

design, cylinder bore distortion and ring conformability on oil consumption

were discussed by Wacker et al. (1978), McGeehan (1979), and Essig et al.

(1990). Simulation models of oil consumption were developed by Maekawa

et al. (1986) and Audette and Wong (1999).

Piston ring friction is affected by many operating and design parameters,

such as lubricant viscosity, piston sliding speed, gas load, ring tension, ring

face prole, ring width, number of rings, ring static and dynamic twist,

piston tilting and ring inclination, bore distortion, ring conformability,

surface roughness of the ring and cylinder liner, break-in, and the quantity

of lubricant available (oil starvation). The piston ring pack friction force

increases with engine speed mainly due to the increase in hydrodynamic

lubrication friction. As the engine load increases, the higher gas pressure

on the back of the compression rings increases the friction force around

the TDC and the BDC in the mixed lubrication regime, but the higher oil

temperature and lower viscosity decrease the friction force at the mid-stroke

in the hydrodynamic lubrication regime. Oil lm thickness measurement at

different loads was reported by Tamminen et al. (2006).

In EGR diesel engines, the piston friction force in the second half of the

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