friction characteristics of piston rings in a reciprocating engine

20
T. Hamatake Oita Kitahara and Y. Wakuri University, Japan T. Kyushu University, Fukuoka, Japan, and M. Soejima Kyushu The performance of a reciprocating engine can be improved by reducing the friction between piston rings and cylinder liner, which significantly contributes to the mechanical friction losses of an engine. The friction force of a piston ring pack is calculated, based on hydrodynamic lubrication theory, for the piston rings. Calcu- lations were carried out for three sets of conditions. Oil starva- tion is taken into consideration in the calculation of oil-film behaviour for a ring pack. The friction characteristics of piston rings are evaluated using the frictional mean effective pressure. The friction force of a piston assembly is measured experi- mentally by an improved floating liner method. The effects of lu- bricant viscosity and engine speed on friction characteristics are investigated by both calculation and experiment. Abstract Friction Characteristics of Piston Rings in a Reciprocating Engine friction, piston ring, lubrication, hydrodynamic, floating liner, calcu- lation, experiment Keywords The tribology of sliding surfaces between piston rings and cyl- inder liner is one of the most complex phenomena occurring in reciprocating engines, and the tribological problem is becoming more and more severe with increases in engine power. Engine performance can be improved by reducing the friction of the piston assembly, since it significantly contributes to the me- chanical power loss of the engine. Many theoretical and exper- imental studies on the frictional power loss of piston rings have been carried out. The oil-film behaviour of piston rings and the viscous fric- tion of a piston-ring pack can be obtained by solving the Rey- nolds equation that governs the oil-film pressure. It is necessary to impose certain boundary conditions for the oil-film pressure. Many kinds of boundary condition have been pro- I NTRODU CTlO N ~ ~~ Lubrication Science 6-1, October 1993. (6) 21 0954-0075 $6.00 + $2.50

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Page 1: Friction characteristics of piston rings in a reciprocating engine

T. Hamatake Oita

Kitahara and Y. Wakuri University, Japan T.

Kyushu University, Fukuoka, Japan, and M. Soejima Kyushu

The performance of a reciprocating engine can be improved by reducing the friction between piston rings and cylinder liner, which significantly contributes to the mechanical friction losses of an engine.

The friction force of a piston ring pack is calculated, based on hydrodynamic lubrication theory, for the piston rings. Calcu- lations were carried out for three sets of conditions. Oil starva- tion is taken into consideration in the calculation of oil-film behaviour for a ring pack. The friction characteristics of piston rings are evaluated using the frictional mean effective pressure.

The friction force of a piston assembly is measured experi- mentally by an improved floating liner method. The effects of lu- bricant viscosity and engine speed on friction characteristics are investigated by both calculation and experiment.

Abstract

Friction Characteristics of Piston Rings in a Reciprocating Engine

friction, piston ring, lubrication, hydrodynamic, floating liner, calcu- lation, experiment

Keywords

The tribology of sliding surfaces between piston rings and cyl- inder liner is one of the most complex phenomena occurring in reciprocating engines, and the tribological problem is becoming more and more severe with increases in engine power. Engine performance can be improved by reducing the friction of the piston assembly, since it significantly contributes to the me- chanical power loss of the engine. Many theoretical and exper- imental studies on the frictional power loss of piston rings have been carried out.

The oil-film behaviour of piston rings and the viscous fric- tion of a piston-ring pack can be obtained by solving the Rey- nolds equation that governs the oil-film pressure. It is necessary to impose certain boundary conditions for the oil-film pressure. Many kinds of boundary condition have been pro-

I NTRO DU CTlO N

~ ~~

Lubrication Science 6-1, October 1993. (6) 21 0954-0075 $6.00 + $2.50

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

posed for the analysis of piston ring l u b r i ~ a t i o n . ~ - ~ ~ ' - ~ ~ ~ ~ ~ Wak- ~ r i , ~ - ~ Hamilton and Moore,' Dowsong and Ruddy1°-12 employed the Reynolds boundary condition. Using a reciprocat- ing test apparatus that can measure the oil-film thickness be- tween a circular-faced ring specimen and a lain glass plate by means of optical interferometry, Wakuri 1 5 , l l investigated what kind of boundary condition for oil-film pressure is the most rea- sonable for solving the Reynolds equation. It was shown from the experiment that the measured values of oil-film thickness and pressure region are in good agreement with the values cal- culated under the Reynolds boundary condition. This was also confirmed by the experiments of Brown and H a m i l t ~ n . ~ ~ ~ ~ ~ Wakuri7 and Sandal4 calculated the friction force due to vis- cous shear stress in the cavitated region as well as in the pres- sure region.

On the other hand, the analytical method of Dowson,' Ruddy1°-12 and Richez13 is somewhat different from that of W a k ~ r i . ~ - ~ and Hamilton.' They assumed that the oil film re- forms immediately after cavitation occurs and breaks down when the oil-film pressure reaches the outlet pressure. Dowson and Ruddy calculated the friction force in the three regions of positive pressure, cavitation and oil-film reformation, while Richez estimated the additional friction force in the cavitation region on the trailing side of the ring.

When the piston rings are used as a ring pack, the oil sup- plied to each ring depends on the amount of oil left on the cyl- inder liner by the preceding ring. Brown and H a m i l t ~ n l ~ ? ~ ~ showed that the discrepancy between measured and calculated oil-film thickness in a piston-ring pack is due to oil starvation, and investigated the interaction of two rings. They derived a simple formula for predicting the degree of oil starvation under conditions of oil-flow continuity. Dowson' and Ruddy1°-12 also considered that the interaction between individual rings is de- termined by the condition of oil-flow continuity, and calculated the oil-film behaviour of a complete ring pack allowing for oil starvation.

From the measurement of the instantaneous friction force of a piston assembly under firing conditions in an engine, much information on the friction characteristics of piston rings has been provided. As a means of measuring the friction force, the instantaneous IMEP methodlg and the floating liner method or movable bore method7~13*20-28 have been developed. In the lat-

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

ter commonly used method, the liner is isolated from the cylin- der head and the cylinder block so that it can move only in an axial direction. The floating liner is held by an elastic support. Although the friction force acting on the liner can be directly measured in this method, the accuracy of measurement is high- ly dependent on the method of support of the liner and on com- bustion gas sealing in the combustion chamber, without impeding the axial movement of the liner. The supporting ar- rangement of liner and the gas sealing device in conventional methods can affect the axial displacement of the liner. Mollen- h a ~ e r ~ ~ used two hydrostatic bearings which act as a gas seal, and a radial supporter for the floating liner. The equipment has the advantage that the floating liner is permitted t o move free- ly in the axial direction and is isolated from the cylinder head since it is a non-contact device. Sherringtona7 and Wakuri7 de- veloped an improved floating liner method with a hydrostatic bearing.

In the present study, three sets of conditions are used to calculate the friction force of a ring pack for fully flooded and starved oil conditions. The results calculated are compared with experimental results obtained using the improved floating liner method equipped with a hydrostatic bearing.

B D Notation

F h

N P P1 P2

h0

pe Pf Pg Q S

- U V vh

axial width of the ring bore diameter friction force oil-film thickness minimum oil-film thickness rotational speed of engine oil-film pressure pressure above a piston ring pressure below a piston ring surface pressure of the ring frictional mean effective pressure gas pressure behind the ring axial oil-flow rate stroke temperature of cylinder liner sliding velocity of ring mean piston speed velocity of the ring normal to the sliding direction stroke volume

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

x,y coordinates X piston displacement P oil viscosity 9 crank angle 0" top dead centre T~ viscous shear stress

The Reynolds equation is employed to determine the oil-film behaviour of piston rings. The theory implicitly involves as- sumptions made to derive the Reynolds equation. The following assumptions are added:

THEORY: basic equations

1. Lubrication is hydrodynamic over the complete piston stroke. 2. Oil is available for the hydrodynamic equations to apply. 3. There is circumferential symmetry, so that the analysis may be treated as if it were one-dimensional. 4. The lubricant is incompressible, and its viscosity does not change along the ring surface. 5. The ring does not tilt in its groove.

From the above assumptions, the Reynolds equations can be written as follows.

- d ( h 3dP -) = 6pU- d h + 12pV d x d x dx

The following force-balance equation in the radial direction has to be satisfied if the friction between ring and groove is t o be neglected.

Even if the leading ring is fully flooded with oil in a ring pack, the subsequent rings will frequently operate in a starved con- dition. Brown and Hamilton18 and Dowsong considered that the interaction between the rings in a ring pack is determined by the condition of oil-flow continuity if the oil is neither sup- plied nor extracted from between the rings. The following rela-

Oil starvation

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

tion between the preceding ring and the subsequent ring, based on the condition of oil-flow continuity, is d e r i ~ e d . ~

Qp 2 Qs (3)

where subscripts P and S denote the preceding ring and the subsequent ring respectively. The condition of oil-flow continu- ity for the top ring on the upward stroke is as follows.

QUP-STROKE -S QDOWN-STROKE (4)

The leading edge of the oil film for the subsequent ring can be determined by the same relationship.

The oil-film pressure distribution can be obtained from the Reynolds equation, eq. (l), by imposing certain boundary con- ditions. The Reynolds boundary condition is employed for the oil-film pressure in the present study. Figures 1 and 2 show the schematics of the hydrodynamic lubrication model pro- posed by references 5 and 9.

The friction force due t o viscous shear stress acting on the cylinder liner is calculated using eq. (5 ) .

Boundary conditions and friction force

It is assumed that, in the cavitated region, the clearance space between a ring and a liner is composed of alternate fingers of oil and air across the ring width. Therefore, the friction force in the cavitated region may be estimated by determining the frac- tion of the ring width over which the oil film is present, from the oil-flow continuity consideration.

Considering the effects on the friction force of the oil-film reformation and viscous shear stress in the cavitated region, the following three cases can be calculated. Case A The oil film breaks down according to the following re- lationship, as shown in Figure 1.

p = p l , dp/dx: = 0 (6) The friction force is estimated from two regions of I and I1 in Figure 1.

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....................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 1 Hydrodynamic lubrication model5

Figure 2 Hydrodynamic lubrication modelg

Case B The oil-film pressure distribution consists of three re- gions of full film, cavitation and full film reformation as shown in Figure 2. The boundary conditions are expressed as follows:

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

p = d p / d x = 0 (7)

The oil-film pressure in the region of oil-film reformation I11 is determined by consideration of the oil-flow continuity and out- let pressure. The friction force is obtained by integrating the shear stresses in each of three regions.

Case C The boundary conditions are as for case B, while the friction force of the cavitated region IV on the trailing side of the ring in Figure 2 is added.

The friction mean effective pressure Pf is defined as fol- lows.

P, = fFdX/V,, (8)

The numerical calculations are conducted with reference to the piston rings of a 4-stroke cycle diesel engine. The piston ring pack consists of two compression rings and a two-land type oil- control ring. The upper compression ring is a plain ring with an axial rectangular cross-section with chamfered edges. The low- er compression ring is a taper-faced ring with an undercut. The axial shapes of the compression rings are assumed, for the top ring, to have a symmetric barrelled face, while the second ring has a composite profile of tapered and barrelled faces. The land shape, in the case of the oil-control ring, is treated as a half-bar- relled profile. The barrel-faced profiles of the rings may be ap- proximated by a parabolic curve. The calculation conditions are given in Table 1. Figure 3 shows the changes of gas pressures,

CALC U LATlON

Table 1 Calculation conditions for piston rings

Compression ring

Top ring 2nd ring

Oil ring

Ring width rnrn Contact width mrn Surface pressure kPa Profile factor rn-’

3 2.5 5 2.4 0.55 0.5 150 110 1600 1.67 7.27 4

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 3 Combustion chamber and inter-ring gas pressures

p1 andp2 with crank angle in the combustion chamber and the inter-ring space. The inter-ring gas pressure is predicted by the Englisch method.

Oil-film behaviour and the friction force for the three cases were calculated. The compression rings are assumed to operate in a starved lubrication condition, although in opera- tion the oil ring is assumed to be fully filled with oil over a com- plete cycle. As to the oil ring, the oil-film behaviour of case A is identical to that of case B since the oil film does not reform, while the friction forces are calculated according to each ana- lytical method. The results calculated are shown in Figures 4 to 6. The oil-film behaviour of the two compression rings is very similar to that of the oil ring, in spite of the different operating conditions. The oil films are very thin over a complete cycle and the cyclic change in oil-film thickness is small. Moreover, the difference of oil-film behaviour between the strokes is small. These features are independent of oil-film boundary conditions. Figure 5 (see overleaf) shows the change in oil-film extent with piston displacement for the top compression rings. The inlet

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10 1 I 1 I I f 1 st ring 2nd ring

- _ _ _ _ _ _ , Oil ring -

-- ---_ .. - 5

,c--

T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 4 Changes of mini- mum oil-film thickness with crank angle (starved lubrication, p, k 0 . 1 2 Pam)

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 5 Oil-film extent (p U=0.12 Pa.m)

Intake Case A

I

case B

-0.5 0 0.5

Compression

-0.5 0 0.5

Power

-0.5 0 0.5 Ring width x/B

Exhaust

- -0.5 0 0.5

~~ ~

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 6 Friction force of a ring pack @tawed lu- brication, p k0.12 Pam)

150 I I 1 I I [ - case A

Crank angle (deg)

region of the ring is partially filled with oil and the oil-film is built up only at a central part of the ring round-off face over a major part of the ring stroke.

Although there is little discrepancy between the oil-film behaviour of case A and case B, the friction force of the ring pack is considerably affected by the analytical method used, as shown in Figure 6. The maximum friction force of case C is the largest of the three cases. The difference of case B and case C is due to the viscous shear stress in the cavitation region on the trailing side of the ring. Comparing Figures 6 and 7 (see over- leaf), the friction force under starved lubrication is much larger than that under fully flooded lubrication, because the average and the cyclic changes in oil-film thickness are very small in the case of starved lubrication. It can be seen that the oil star- vation has a remarkable effect on the friction force of a ring pack.

Figure 8 (see overleaf') shows the relation between the frictional mean effective pressure, Pf, and the product of the oil viscosity p and the mean piston speed g , p g . "he Pfvalue can

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 7 Friction force of a ring pack (fully flooded lubrication, p k 0 . 1 2 Pa.m)

Crank angle (deg)

be correlated in the form of ( ~ 3 ) " . The exponent on the p u is approximately 0.48 in the case of starved lubrication, while be- ing 0.64 in the case of fully flooded lubrication. Regarding case C, the Pfof the starved lubrication is two times larger than that of the fully flooded lubrication.

A schematic of the test equipment is shown in Figure 9 (see overleaf). As a means of measuring the friction force of the pis- ton assembly under firing conditions, we adopted the improved floating liner method, since the conventional floating liner method may restrict the axial movement of the liner. The fric-

EXPERIMENTAL: Experimental apparatus and procedure

tion force acting on the cylinder liner can be detected by isolat- ing the cylinder liner from the cylinder block and the cylinder head. The floating liner is constrained radially by hydrostatic bearings and thus is permitted to move freely in the axial direc- tion. The axial force acting on the liner is measured by a piezo- electric load sensor.

This method requires the liner to be isolated from the in- fluence of the pressure in the combustion chamber, since the

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 8 Relation between Pf and p U (S-starved lu- brication, FF-fully flood- ed lubrication)

6o r

-

S

case C

10 I I I I I I I .- 0.06 0.1 0.2

F G Pam

cylinder liner is not in contact with the cylinder head. After a few attempts to establish an effective gas seal, an extremely thin rubber sheet has been adopted as the sealing d e ~ i c e . ~ Fig ure 10 (see overleaf) shows the detail of the gas sealing meth- od. With these improvements, the friction force can be measured with higher ac~uracy .~ A single cylinder 4-stroke cy- cle diesel engine is used for the present test. The specifications are shown in Table 2 (see p. 36).

A ring pack contains three compression rings and two oil rings, and is tested after complete running-in. The specifica- tions of the piston rings are shown in Figure 11 (see overleaf). An SAE 30 CD-level engine oil was used for the lubricating oil and the hydraulic oil. A representative temperature of the lin- er, T', is measured with a thermocouple located at the centre of the top ring stroke. The oil viscosity p is estimated from T,.

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 9 Schematic of an improved floating liner method

fl 8

1 T T

t

I . Piston

I

!. Gas seal rubber sheet 1. Cylinder liner C. Hydrostatic bearing 5. Piezo load sensor 5 . Spherical bearing 7. Hydraulic pump

8. Supply of hydraulic oil 9. Drain of hydraulic oil

10. Hydraulic oil tank 11. Oil cooler 12. Pump 13. Charge amplifier 14. Oscilloscope

~~

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 10 Schematic of gas sealing (dim. in mm)

Rubber sheet

ent

Detail of A

Figure 11 Specifications of a ring pack (dim. in mm)

I ~~

Top ring Compression ring

2nd ring 3rd ring 4.5 fE> &* N

Pe = 182kPa Pe = 146kPa Pe = 235kPa

Oil ring 1st oil ring 2nd oil ring

A s

Pe = 467kPa Pe = 421 kPa

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Table 2 Specifications of the test engine

Type of engine 4-stroke cycle diesel engine

No. of cylinders 1

Bore diameter 105 mm

Stroke 120 mm

Compression ratio 19

Output power 6 kW/1400 r/min

Total displacement 1.039 L

Connecting rod length 220 mm

No. of piston rings 3 compression rings 2 oil rings

Cylinder lubrication method Splash lubrication

Figure 12 shows a typical cyclic change of friction force for a piston assembly with five rings measured under firing condi- tions. It is seen that the largest friction forces occur at the ring reversals, particularly at the end of the compression stroke and at the beginning of the expansion stroke. This is different from the calculated results based on hydrodynamic lubrication. The piston assembly operates in the regime of boundary lubrication at the beginning of the stroke since the oil film is too thin to en- sure hydrodynamic lubrication. Although the friction forces at both ends of the stroke are large, they hardly affect the friction- al mean effective pressure. As the piston moves towards the mid-stroke region, the friction force decreases with the increase of piston speed. The operating conditions of the piston assem- bly presumably vary from boundary lubrication to mixed lubri- cation, and then to the fluid-film lubrication. The friction forces in this region contribute significantly to the frictional mean ef- fective pressure and are mainly due to the viscous shear stress which increases with the increase of oil viscosity and engine speed.

Figure 13 (see overleaf) shows the relation between Pf and PO. The experimental values of Pfincrease with increasing

Experimental res u I ts

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~

T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 12 Typical friction diagram (Intake) (Compression) (Power) (Exhaust)

400 1

Crank angle, 0 (deg)

p a as do the calculated results. The exponent p a obtained from the correlation equation is 0.4. The calculated results based on case A are also indicated in Figure 13. These results under starved lubrication conditions give values comparatively close to the experimental results.

The number of piston rings was decreased from five to three, to examine the influence of the number of piston rings on friction. A ring pack with three rings is composed of two com- pression rings and an oil ring. As a means of reducing the fric- tion loss, this appears to be an effective measure as shown in Figure 14 (see overleaf). However, it should be noted that the lubrication conditions for the top compression ring becomes more severe as a result of decreasing the number of compres- sion rings, since the gas pressure acting on the top ring increas- es . 7

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Figure 13 Relation between Rand F (S-starved lubri- cation, FF-fully flooded lu- brication)

Figure 14 Influenceof number of rings (p U=O.1 Pam)

I Calculated (case A) - Experimental

100

80

60

si !i

L‘ 4c

2( (

#.-””’.- Experimental

Calculated (S)

I I I I I I I I I I I I4 0.05 0.10 0.1!

P G Pa.m

No. of rings Pf 50

kPa 100

I I I I

5 rings 3 com. + 2 oil

I

3 rings 2 com. + 1 oil

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T. Hamatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

The results obtained in the present study can be summarised as follows. CONCLUSION

1. From the analyses of oil-film behaviour for a complete ring pack considering oil starvation, it is found that the oil-film be- haviour of the compression rings is dominated by that of the oil ring, and this leads to similar cycles of oil-film thickness for the compression rings. The discrepancy due to boundary conditions used in the present study is small. 2. The inlet region of the rings under starved lubrication is only partially filled with oil, and the oil-film region is built in the central part of the ring face over a major part of the ring stroke. 3. Oil starvation has a remarkable effect on friction force of the ring pack, which becomes considerably larger, since the aver- age and cyclic change of the oil-film thickness is extremely small. The friction force differs, depending on the analytical method used as the viscous shear stress in the cavitation region along the ring face is large. 4. The friction characteristics of a piston assembly under firing conditions can be clearly resolved using the improved floating liner method. It is found that the frictional mean effective pres- sure Pfincreases with the increase of the product of the oil vis- cosity and the mean piston speed pu, and can be correlated in the form of (pu)”. The exponent on pg is about 0.48 in the starved lubrication analysis and 0.4 in the experiments. 5. Decreasing the number of piston rings is an effective means of reducing friction loss. The authors would like to acknowledge Mr. M. Ohtsubo of Ky- ushu University and Mr. F. Shimada of Oita University for their kind cooperation.

Acknow’edgement

1. Eilon, S., and Saunders, O.A., ‘A study of piston ring lubrication’, froc. 1. Mech.

2. Furuhama, S., ’A dynamic theory of piston ring lubrication (first report- calculation)’, Bull. JSME, 2, 423 (1959). 3. Lloyd, T., ‘The hydrodynamic lubrication of piston rings’, Proc. 1. Mech. E., 183,

4. Ting, L.L., and Mayer, J.E., Jr., ‘Piston ring lubrication and cylinder bore analysis, Part I -Theory’, Trans. ASMESer. F; 96,305-14 (1974). 5. Wakuri, Y., Soejima, M., and Taniguchi, T., ‘On the oil-film behaviour of piston rings (correction of effective pressure region of oil-film)’, Bull. JSME, 21, 295-302 (1 978). 6. Wakuri, Y., Ono, S., Soejima, M., and Taniguchi, T., ‘Oil film behaviour of a circular faced slider in reciprocating motion’, froc. JSLE-ASLE lnt. Lubr. Conf., Elsevier, 1975, pp. 419-27. 7. Wakuri, Y., Soejima, M., Kitahara, T., Wada, S., and Ohtsubo, M., ‘Studies on the characteristics of piston ring friction’, Memories of the Faculty of Engineering

References E., 171, 427-33 (1957).

28-34 (1968).

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T. Harnatake, T. Kitahara, Y. Wakuri, M. Soejima: Friction Characteristics of Piston Rings in a Recip- rocating Engine

Kyushu University, 50, 251-75 (1 990). 8. Hamilton, G.M., and Moore, S.L., ‘Comparison between measured and calculated thickness of the oil-film lubricating piston rings’, Proc. l. Mech. E., 188,

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Paper originally presented at Technische Akademie Esslingen, 8th International Colloquium, ‘Tribologie 2000’, 14-16 Jan. 1992

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