Tribology Transactions, 47: 17-22, 2004 C Society of Tribologists and Lubrication Engineers Copyright  ISSN: 0569-8197 print DOI: 10.1080/05698190490279074

Modeling of Abrasive Wear in a Piston ✐Ring C and Engine Cylinder Bore System SIMON C. TUNG (Member, STLE) General Motors Research and Development Center Chemical and Environmental Sciences Lab Warren, Michigan and YONG HUANG Georgia Institute of Technology School of Mechanical Engineering Atlanta, Georgia

Engine-related improvements such as more efficient engine components, improved engine oils, and high-performance coating materials, need to be verified in terms of their effects on the tribological performance of the piston ring/cylinder bore system. The main purpose of this research is to develop an abrasive wear model for the piston ring/cylinder bore system during steady-state operation by considering the effects of temperature, load, oil degradation, surface roughness, and material properties. The model can be used either in theoretical modeling or integrated with finite element analysis. Based on a laboratory simulator, a three-body abrasive wear model has been developed to model the wear progression of the piston ring/cylinder bore system during steady state operation. The proposed novel abrasive wear model addresses the effects of temperature, load, oil degradation, surface roughness, and material properties. The feasibility of the proposed model is illustrated by a numerical example.

ity in terms of power loss, fuel consumption, oil consumption, blowby, and even harmful exhaust emissions. The wear rate of the piston ring/cylinder bore system is high initially, decreases afterward, then reaches a steady state. Ring/bore wear ultimately results in poor performance and decreased oil economy, eventually requiring an engine overhaul. Use of real engine tests for the evaluation of tribological performance is very costly and time consuming. One way to speed up the process, while maintaining accuracy of the prediction, is to develop mathematical models for each wear mechanism. Like any other complicated physical system, several wear mechanisms contribute to the wear progression for the piston ring/cylinder bore system. As reviewed by Becker, et al. (1), the three important wear mechanisms mentioned over the years are: corrosion, abrasion, and adhesion. Corrosion is the dominant mechanism when the engine runs either very cold or very hot. Abrasion results from the cutting and plowing action of hard particles. Adhesion is usually described as occurring when the oil film between the ring and the bore is so thin that metal-to-metal contact occurs. Other wear mechanisms, such as oxidation and splat delamination (Becker and Ludema (2)), have been reported also. Generally, corrosion has been successfully reduced by the use of thermostats and by the addition of corrosion inhibitors to engine oils (1); abrasion and adhesion are common during the running-in period because of the surface roughness of both the ring and the bore; abrasion, oxidation, and delamination wear are the main mechanisms during the steady-state period. Whatever the main wear mechanisms are for a specific piston ring/cylinder bore system, the total wear volume loss for both the ring and the bore is the sum of the contribution from each mechanism that is observed. The real wear progression of the piston ring/cylinder bore system is quite complex and is a function of several factors, such as metallurgy of the contacting materials, surface finish and integrity, operating conditions of the components, and lubricant properties. Although the piston ring/cylinder bore wear progression has received intensive attention in the literature, only a few researchers have attempted to model the wear of the piston ring and/or cylinder bore (Gangopadhyay (3)), considering the large

KEY WORDS Abrasive Wear; Engine Oils; Piston-Rings

INTRODUCTION To meet tough automotive competition and stringent government regulations, more efficient engine components, improved engine oils, and high performance coating materials have been developed within the automotive industry. As part of the overall performance evaluation of these developments, the tribological performance of the ring/bore system must be determined. In an internal combustion engine, the tribological performance of the piston ring/engine cylinder bore system has long been recognized as important in achieving desired engine efficiency and durabilPresented at the STLE/ASME Tribology Conference in Ponte Vedra Beach, Florida October 27-29, 2003 Final manuscript approved August 19, 2003 Review led by Gary Barber

17

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S. TUNG AND Y. HUANG

NOMENCLATURE A Acontact a d d0 dt Fparticle f K, K0 Kabrasion Kˆ abrasion Kdegradation Kroughness L N Nparticle

= amplitude of the stroke = contact area between the piston ring and the cylinder bore = constant = wear depth = wear depth during the running-in phase = time interval = force supported by the abrasive particle = sliding frequency = constants = process related abrasive wear coefficient = process related abrasive wear coefficient considering the effects of surface roughness and oil degradation = wear coefficient modification due to oil degradation = wear coefficient modification due to the surface roughness = piston ring width = normal load = number of total generated wear particles within a time interval

literary body of experimental investigations on this issue. To the authors’ knowledge, most of the proposed models simply used Archard’s abrasive wear equation or a modified form of this equation (Gangopadhyay (3); Tingand Mayer (4); Visscher, et al. (5); Priest et al. (6)). These documented models are insufficient to address the wear progression of the piston ring and/or cylinder bore. A successful wear model should include variables from hydrodynamics, contact mechanics, materials engineering, and chemistry (Ludema (7)). Abrasion is generally considered to be a dominant wear mechanism for the piston ring/cylinder bore system. In this work, modeling of abrasive wear for the steady-state period will be addressed in detail. The proposed novel abrasive wear model addresses the effects of temperature, load, oil degradation, surface roughness, and material properties. The feasibility of the proposed model will be illustrated by a numerical example. The model can be further applied in theoretical modeling or integrated with finite element analysis. To fully model the wear progression, adhesive wear, oxidation, and delamination should also be included and modeled in addition to abrasive wear, depending on observed wear patterns for a specific coated or uncoated piston ring/cylinder bore system and the specified operating conditions (running-in or steady state). These issues will be addressed in a future investigation. In researching the wear progression of the piston ring/cylinder bore system, the use of a laboratory simulator, such as a reciprocating machine, has been verified as an effective approach (Becker and Ludema (1); Barber, et al. (8)). In this study, abrasive wear of the piston ring/cylinder bore system is modeled based on such a simulation and this approach is illustrated by a numerical example.

nparticle n P Pa Pt Pw pabrasion % T (◦ C) t t0 V(t) Vwear-abrasion Vˆ wear-abrasion

w x λ θ

asperities or perhaps hard particles trapped at the interface. Assuming abrasive wear is a process in which a hard sharp indenter scratches along the surface of a softer counter workpiece, the workpiece volume loss Vwear-abrasion due to abrasive wear can be expressed as: Vwear-abrasion =

Abrasive wear is damage to a component surface that arises because of the motion relative to that surface of either harder

x N tan θ 3Pw

[1]

Equation [1] is similar to Archard’s wear equation, which asserts that wear volume loss is directly proportional to the load, but inversely proportional to the surface hardness of the wearing material. If wear depends on the presence of free wear-particles, the main mechanism is called three-body abrasion. If the wear-producing agent is the hard counterface itself, or the abrasive particle is constrained within the counterface, it is called two-body abrasion. For a three-body condition, by using a lapping machine with the abrasives between two sliding surfaces, Rabinowicz, et al. (9) developed empirical wear volume loss equations as a function of the sliding distance (x), the normal load (N), the average roughness angle of the abrasive particle (θ ), hardness of both base wearing material (tool or workpiece), and the abrasive particle as Eq. [2]. By incorporating material hardness data, the model can be applied in the piston ring/cylinder bore system.

MODELING OF ABRASIVE WEAR FOR PISTON RING/CYLINDER BORE SYSTEM Two-Body and Three-Body Abrasive Wear Mechanisms

= number of particles in the unit apparent contact area = constant = uniform pressure between the ring and the bore = hardness of the abrasive particle = hardness of the piston ring or the cylinder bore = hardness of the workpiece = the percentage of total normal force support by abrasive particles = temperature = elapsed time = the moment when steady-state wear starts = sliding velocity of the piston ring = volume loss due to abrasion within a time interval = volume loss due to abrasion within a time interval during the steady-state period considering the effects of surface roughness and oil degradation or of a particle = piston ring thickness = sliding distance = dimensionless film thickness = average roughness angle of the abrasive particle

Vwear-abrasion =

x N tan θ 3Pt

Vwear-abrasion =

x N tan θ 5.3Pt

Vwear-abrasion =

x N tan θ 2.43Pt

for  

Pt Pa Pt Pa

Pt < 0.8 Pa

−2.5

for 1.25 >

−6.0 for

Pt > 0.8 [2] Pa

Pt > 1.25 Pa

The volume loss model for an abrasive particle can be simplified as:  Vwear-abrasion = K

 Pan−1 x N tan θ Ptn

[3]

Modeling of Abrasive Wear in a Piston Ring and Engine Cylinder Bore System

where n and K are known functions of

1.25 >

Pt Pα

19

defined as follows (10):

Pt < 0.8, Pa

n = 1.0,

K = 0.333

Pt > 0.8, Pa

n = 3.5,

K = 0.189

Pt > 1.25, Pa

n = 7.0,

K = 0.416

[4]

Under some conditions, the hard abrasive particles are securely constrained within one base material, which causes two-body abrasive wear on the counter base material. The hardness of the abrasive particle is commonly assumed to be infinite in modeling the wear loss under a two-body condition, and the volume loss can be expressed as (Rabinowicz (11)): Vwear-abrasion = k

xN 3Pw

[5]

where k is the dimensionless abrasive wear coefficient. For the piston ring/cylinder bore system, the generated abrasive particles are different for the different ring/bore pair. Cavdar, et al. (12) believed that on the bore side there is a layer called the oxide metal mixture (OMM) layer near the bore metal and the organo-iron compound (OIC) layer near the oil film; on the ring side there is the ring chemical layer. Becker, et al. (1) suggested that detachment of oxide flakes is the primary material loss mechanism for the bore. Based on a ferromagnetic method, iron particles and Fe3 O4 with flake geometry were observed from the dynamometer test engines with a cast iron bore or sprayed steel bore on aluminum, and iron oxide flake was also observed from simulator tests of cast iron bores (1). Tung, et al. (2) observed similar iron oxides and iron particles when using a cast iron bore or sprayed steel bore. For cast iron bores, the graphite flakes in the matrix also deform and detach with flake morphology (Cavdar and Ludemal (12)). Fortunately the graphite flakes act as solid lubricants to some degree. During the running-in period, there will be adhesive wear due to metal-to-metal contact. Some abrasive particles are generated as a result of the broken microwelds between the asperities of the ring and the bore. Based on the above discussion, iron and iron oxide with flake geometry are considered to be the main abrasive particles produced in the piston ring/cylinder bore system, and three-body abrasive wear is the main abrasive wear mechanism.

Modeling Three-Body Wear Mechanism for the Piston Ring/Cylinder Bore System The laboratory simulator specified by Tung, et al. (2) is studied here. Considering the condition between the interface of the piston ring/cylinder bore system as shown in Fig. 1, a piston ring with width L and thickness w slides along a cylinder bore longitudinally with speed V(t). Assuming the interface to be a plane with a uniformly distributed pressure P along the interface, the total normal load N on the contact region can be calculated as: N = PwL

[6]

Fig. 1—Schematic of the piston ring/cylinder bore simulator system.

For the piston ring/cylinder bore system, part of the total normal load is supported by microwelds under the adhesive wear mechanism during the running-in period and part is supported by the oil film through hydrodynamics. Assuming pabrasion % of the total normal load is supported uniformly by every particle as Fparticle , and nparticle is the number of particles in the unit apparent contact area, the force balance can be expressed as: Npabrasion % = Fparticle nparticle wL

[7]

Based on Eqs. [6] and [7], Fparticle =

pabrasion %P nparticle

[8]

In predicting the volume loss due to abrasive wear, the rate of oxide formation and removal are assumed equal to simplify the problem. With this assumption, the total number of abrasive particles formed during a time interval is: Nparticle = nparticle Acontact = nparticle wL

[9]

The total sliding length of the piston ring during a time interval dt is approximated as:   x = V(t)dt = Asin(2π f )dt [10] Since the reciprocating cycle is very short (less than 1 second) compared with the time required to change other parameters such as hardness, the average sliding speed is used here. The sliding length during time interval dt can be expressed as: x = 2Af dt

[11]

Assuming the probability of generating a free abrasive particle is equal everywhere along the interface when the piston ring slides along the cylinder bore, the average sliding distance for every possible particle is approximated as x2 = Af dt. Based on the three-body abrasive wear empirical model of Rabinowicz, et al. (9), assuming a uniform temperature distribution along the interface, the total tool volume loss

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S. TUNG AND Y. HUANG

Vwear-abrasion for an ideal piston ring and cylinder bore system during the time interval dt caused by Nparticle particles at an average sliding distance Af dt under the normal load Fparticle is,  n−1   P Vwear-abrasion = Nparticle K a n x Fparticle tan θ Pt  n−1   pabrasion %P P = nparticle wLAf dt K a n tan θ nparticle Pt  n−1   P = wLpabrasion %PK a n tan θ Af dt [12] Pt The model can be further simplified as:  n−1   P Af Kabrasion K a n wLPdt Vwear-abrasion = Pt

Fig. 2—Transition model of wear coefficient modification due to surface roughness.

[13]

where Kabrasion = pabrasion % tan θ is the abrasive wear coefficient. For a given piston ring/cylinder bore system, pabrasion % is different for the running-in period and the steady-state period. Thus, a different Kabrasion should be used for the running-in and the steady-state periods. If there is more than one kind of abrasive particle existing along the interface, the total tool volume loss is made up of contributions from different kinds of abrasive particles. In these cases, the value of Kabrasion associated with each particle is different and needs to be determined experimentally. The hardness of the abrasive particles (metallic iron and/or iron oxide) Pa and the ring/bore Pt can be expressed as an exponential function of temperature (T is in ◦ C): Pa = Pa0 e−Kpa T ,

Pt = Pt0 e−KPt T

[14]

where Pa0 and Pt0 are the hardness of the abrasion particles and the ring/bore measured at a reference temperature, respectively. The flash temperature of the lubricated contacts is indispensable information in determining the hot hardness of bore, ring, and abrasive particle(s), if any. Considering the low coefficient of friction of the piston ring and cylinder bore pair, the flash temperature due to frictional heating is negligible compared with the heating effect of the combustion chamber. To simplify the modeling process, in the bench test, the temperature is stabilized at a set point by a PID controller and considered as a constant under the experimental operating conditions. In a real engine, this temperature varies with the position of the crankshaft during every engine stroke.

Modeling the Effects of Surface Roughness and Oil Degradation At the interface of the piston ring and the cylinder bore, it is possible that a different lubrication regime exists as described by the Stribeck curve, which is defined by a dimensionless film thickness λ (the ratio between the oil film thickness and the composite surface roughness). In the boundary lubrication regime, some abrasive wear is expected to occur due to surface contact. In the hydrodynamic lubrication regime, there should be no abrasive wear because the surfaces are totally separated by an oil film. In the mixed regime, the progress of wear depends on the dimensionless film thickness. To take into account the effect of surface finish, the wear coefficient Kabrasion should be mod-

ified by a factor which is a function of the dimensionless film thickness. As shown in Fig. 2, it is widely assumed that the wear constant or wear coefficient modification decreases linearly as lubrication conditions change from boundary to hydrodynamic (Gangopadhyay (3); Visscher, et al. (5); Bell and Colgan (13)). It can be represented mathematically as: K0

 Kroughness (λ) =

K0

(hb − λ) hb − ha 0

for λ ≤ ha for ha < λ ≤ hb

[15]

for λ > hb

where K0 is a dimensionless coefficient, which is determined by the tribological property of the piston ring/cylinder bore sliding pair. Based on the study of Visscher, et al. (5), ha is taken as 0.5 and hb is taken as 4, so that Eq. [15] can be expressed as: K0

 Kroughness (λ) =

K0

(4 − λ) 3.5 0

for λ ≤ 0.5 for 0.5 < λ ≤ 4

[16]

for λ > 4

Typically the film thickness varies throughout the engine cycle (6), and this variation should be included in the above transition model in modeling the wear progression of the piston ring and/or cylinder bore in a real engine. Under actual engine operating conditions, the lubricant will go from a fresh to a degraded condition mainly due to exposure to combustion products and heat conducted from the combustion chamber. A significant difference in the wear factor has been reported between fresh and degraded conditions of the same lubricant by Priest, et al. (6). Here a linear relationship is used to describe the change of wear coefficient with the degradation of the lubricant as follows: Kdegradation = 1 + at

[17]

Since the temperature along the interface between the piston ring and the cylinder bore is usually about 100◦ C under engine operating conditions, the lubricant degradation rate is assumed not to depend on temperature.

Modeling of Abrasive Wear in a Piston Ring and Engine Cylinder Bore System

21

Modeling of Volume Loss Due to Abrasive Wear Combining the effects of surface roughness and oil degradation, the wear volume loss due to abrasive wear Vˆ wear-abrasion for the piston ring and cylinder bore system during steady-state can be expressed as: Vˆ wear-abrasion  n−1   P = Af Kabrasion K a n wLPKroughness (λ)Kdegradation dt Pt  n−1   P Af Kˆ abrasion K a n wLP(1 + at)dt for λ ≤ 0.5 [18] Pt   n−1  4 − λ  P Af Kabrasion K a n wLP(1 + at)dt for 0.5 < λ ≤ 4  3.5 Pt 0

for λ > 4

where Kˆ abrasion = K0 Kabrasion is the dimensionless abrasive wear coefficient. In order to apply this model, the wear coefficients Kˆ abrasion need to be determined for different piston ring and cylinder bore combinations. The hardness data for the identified abrasive particles can be determined experimentally or found from a metal handbook. The oil degradation rate needs to be calibrated or found from a lubricant handbook.

NUMERICAL EXAMPLE Abrasion has been observed to be the main wear mechanism when sliding a molybdenum ring over a plateau-honed, smooth iron cylinder bore (Tung and Emley (2)). To illustrate the proposed model, the wear progression of the cylinder bore is discussed here based on the experimental results of Tung and Emley (2), which were obtained by using a Cameron Plint–based laboratory simulator. A typical worn cylinder bore and the corresponding wear profile are shown in Figs. 3 and 4, respectively. The test conditions used were:

Fig. 4—Wear profile of a typical cylinder bore (A-A view based on Fig. 3).

Duration Temperature Stroke Frequency Load Oil

2, 5, and 10 hours 125◦ C 6.77 mm 10 Hz 80N SAE 5W-30

For the Cameron Plint simulation system used (Tung and Emley (2)), the thickness of the piston ring is negligible compared with the stroke of the system. If the running-in process finishes at time t0 , by ignoring changes in the operating condition and the effect of the temperature variation on the material hardness during every stroke during the steady-state period, Eq. [18] can be rewritten as follows: Vˆ wear-abrasion  n−1   t P = Af Kroughness (λ)Kabrasion K a n wLP(1 + at)dt Pt t0  n−1  P = Af Kroughness (λ)Kabrasion K a n Pt   1 1 ×wLP t + at 2 − t0 − at02 [19] 2 2 Here the wear depth of the cylinder bore is of interest. By treating the interface as a plane, the wear depth d at time t can be expressed as: Vˆ wear-abrasion d = d0 + = d0 + w P f Kroughness AL   n−1  1 P 1 t + at 2 − t0 − at02 [20] (λ)Kabrasion Kabrasion K a n Pt 2 2 For illustration purposes, the degradation rate constant (Eq. [21]) in Eq. [17], which is estimated based on the work of Priest, et al. (6), is used ignoring any possible difference between the oils used. In estimating the above degradation rate, the other conditions in the previous work (6) are assumed unchanged when the lubricant goes from a fresh to a degraded condition. a = 0.0958 (1/hour)

Fig. 3—A typical tested cylinder bore with two separate worn surface areas.

[21]

For the molybdenum ring and plateau-honed smooth iron bore pair, it is found that the average friction coefficient varies within ±2% over the 20-hour run (Tung and Emley (2)). Based on this observation, it is assumed that the lubrication film thickness has not changed during the investigation for simplicity, that is, Kroughness

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S. TUNG AND Y. HUANG

piston ring/cylinder bore system during steady-state operation. The proposed abrasive wear model addresses the effects of temperature, load, oil degradation, surface roughness, and material properties. The feasibility of the proposed model is illustrated by a numerical example. The model can be further applied in theoretical modeling or integrated with finite element analysis. To fully model the wear progression, lubricant oxidation and surface delamination should also be included and modeled in addition to abrasive wear, depending on observed wear patterns for a specific coated or uncoated piston ring/cylinder bore system and the specified operating conditions (running-in or steady state). Combining the effects of surface roughness and oil degradation, the wear volume loss due to abrasive wear has been investigated. Based on this model simulation, the wear rate of the engine cylinder bore system is also calculated. The increases in the wear rate at longer times are attributed to the high oil degradation rate used in this simulation. Fig. 5—Wear depth progression of the iron cylinder bore.

ACKNOWLEDGMENTS

is considered constant here. Since the temperature is controlled at 125◦ C in the tests, the hardness of both the bore and the abrasive particles (iron oxide here) is considered unchanged as Eq. [14]. Further, K is constant as well since it depends on the hardness of the bore and the abrasive particle as defined in Eq. [4]. Kabrasion is a constant for the given piston ring/bore system during the steady-state period, which can be determined experimentally Pn−1 using a pin-on-disc test. So w P f Kroughness (λ)Kabrasion K( Pa n ) of t Eq. [20] is treated as a constant and determined as 0.0041 using a curve-fitting technique based on the measurements (Tung and Emley (2)). Based on the observation (2), steady-state wear conditions were reached after 5 hours of running. Based on the characteristics of the simulator system (2), the wear depth of the iron bore during the steady-state operation is approximated as (the runningin wear depth is included as 0.7664 µm): d = 0.7664 + 0.0041(t + 0.0479t 2 − 2.6042)

[22]

Based on Eq. [22], the wear depth progression of the iron bore is calculated and shown in Fig. 5. The increases in the wear rate at longer times are attributed to the high oil degradation rate used in this simulation.

SUMMARY Modeling of the wear progression of the piston ring/cylinder bore system is critical for advancing engine-related technologies. Based on a laboratory simulator, a three-body abrasive wear model has been developed to model the wear progression of the

The authors thank Drs. Michael L. McMillan and James A. Spearot for their support. The authors also acknowledge the help of Mr. Angelo G. Quintana.

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