A Chemical Kinetics Model to Predict Lubricant ... - Springer Link

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Tribology Letters, Vol. 14, No. 2, February 2003 (# 2003 )

A chemical kinetics model to predict lubricant performance in a diesel engine. Part I: Simulation methodology Chun-I Chena and Stephen M. Hsub a

b

University of Maryland, College Park MD National Institute of Standards and Technology, Gaithersburg, MD

Received 3 March 2002; accepted 19 May 2002

The ability of a lubricant to protect increasingly complex diesel engines directly affects engine durability and warranty costs and is becoming increasingly costly to validate. This paper presents a novel approach combining a chemical kinetic model using rate constants determined by a set of laboratory bench tests and a finite-difference computer program to predict lubricant performance in a given diesel engine. The computer program takes into account the engine’s mechanical design, such as temperature, pressure, oil flow rate, top ring zone volume, and other parameters. The chemical kinetic model incorporates the kinetic rate constants determined for that particular lubricant in a set of special bench-test procedures tailored to a particular engine and its operating conditions. The bench-test procedures take into account the necessary environment in that particular engine such as specific metal catalysis, oxidation conditions, and deposit formation. The computer program then combines the lubricant degradation model with the engine operating sequence to yield a predictive simulation. This approach is capable of predicting the amount of deposit in the top ring groove and the amount of oil consumption in that engine. The computer program models the engine as three chemical reactors in series. The three reactors are: the oil sump, the top piston ring groove, and the piston cylinder-liner interface. Oil flows from the sump to the piston rings and to the piston liner area. The oxidation process is described by a set of simplified chemical kinetic rate equations. The kinetic constants of the lubricant are determined by laboratory bench-test procedures using Differential Scanning Calorimetry (DSC), a Thermal Gravimetric Analyzer (TGA), and the Micro-Oxidation test apparatus. The design and the operating conditions of the engine define the chemical reaction conditions used in the simulation program such as the temperatures of the reactions, the residence time in a particular reactor, the volume of the reactors, and the operating sequence of the engine. The simulation program is validated by the Caterpillar 1K engine dynamometer test results. Two experimental high-temperature lubricants and three IK reference oils were used in this study. Good agreement between model simulation and 1K engine test results was obtained. KEY WORDS: diesel engines, lubricant performance, kinetic model, prediction, engine deposit, oil consumption

1. Introduction In the heavy-duty diesel industry, the drive toward zero emission, high-energy efficiency engines (LE 55, a low-emission 55% energy-efficient engine), and onemillion miles’ durability demands new materials and innovative technologies to meet these goals. New engine development is an expensive and time-consuming undertaking. Oftentimes, the long-term durability of the engine is controlled by the materials used, the mechanical design, and the effectiveness of the lubrication. Historically, bench simulation tests are used to evaluate materials in combination of existing lubricants. Single-cylinder ‘‘bench tests’’ incorporating new materials or designs are conducted on an engine dynamometer to screen materials and designs. If successful, the materials and design are then tested in a prototype engine. If the material or design is significantly different from past experience, then a fullscale field test will be conducted to evaluate the longterm durability and material compatibility. Long-term lubricant-materials compatibility and durability issues often emerge at the last stage. This is expensive. Conversely, given an engine design, what kind of lubricant

is needed to achieve satisfactory performance is difficult to ascertain at the beginning. From the lubricant developers’ perspective, since the new engine is evolving, many parameters have not been set and therefore it is difficult to define the lubricant needs for new engines. This leaves the lubricant developers with very little data to proceed with until the engine is sufficiently developed so that it can be made available for lubricant testing. At this time, however, many of the parameters including the materials have been fixed, and optimum lubrication may or may not be feasible. A case in point is the Low Heat Rejection Engine development. Because of the lack of effective high-temperature lubricants, the engine temperature had to be revised downward, compromising the potential benefits of the concept. Another issue is the warranty costs associated with current production engines. The use of proper lubricants for a given engine design and operating conditions is vital in controlling the warranty costs. What lubricant is best for each engine operation and at what performance level the lubricant needs to be are issues the current engine manufacturers face. Current engine tests designed to qualify lubricants are becoming increasingly 1023-8883/03/0200-0083/0 # 2003 Plenum Publishing Corporation

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C.-I. Chen, S.M. Hsu/Chemical kinetics model to predict lubricant performance in a diesel engine. Part I

costly and complicated. Proper laboratory bench tests coupled with an analytical model can serve as a valuable aid to reduce the guesswork associated with the lubricant qualification testing. An analytical model that is capable of predicting lubricant performance based on properties of lubricants and materials will significantly alleviate some of these issues.

2. Basic concept The performance of a lubricant in a diesel engine is governed by both the mechanical and chemical processes. If the chemical processes can be modeled by a chemical kinetic model and the mechanical processes can be simulated by a finite-difference computer model as a function of time, then at least in theory, any engine operation can be modeled. The key is how to allow for the interaction pattern between the chemical model and the mechanical model so that the results of an engine test or an engine operation can be reasonably predicted. Since there are many chemical and mechanical processes in an operating engine, and many of the processes are well understood for mathematical modeling, only some of the key results can be predicted. So this paper should be viewed as the first step in fully simulating an engine performance. For a given engine design, the lubricant interacts with the materials, combustion products, engine blow-by, and the air under a variety of temperatures, pressures, and loading conditions. The lubricant undergoes different reaction conditions depending on where the oil is. The engine can be reasonably represented by three chemical reactors in series: the oil sump (reactor 1), where the temperature is low; the piston top ring groove zone (reactor 2), where the temperature is high; and the piston cylinder-liner (reactor 3) interface, where the temperature is the highest. The flow rates among the reactors are controlled by the engine operating conditions and the specific ring gap specifications, tolerance, etc. The volume and residence time of the lubricant in each of the reactors are somewhat problematic to determine precisely. Fortunately, the work conducted by Fox [1], who determined the average residence time of lubricants in the top ring groove experimentally, provided important information for a reasonable basis to estimate the residence time of a lubricant at the top ring groove in an operating diesel engine. A simplified first-order kinetic equation has been proposed in describing the lubricant degradation processes [2]. The equation describes the oxidation process in terms of the initial hydrocarbon concentration, primary oxidation products, high-molecular-weight polymers, and the oil-insoluble deposits. The key for different lubricants therefore is the rate of reactions. If the reaction rates can be determined independently in a

set of controlled laboratory bench tests which take into account the key chemistries, metal surface catalysis, and engine operating environment, then this set of kinetic equations can be solved using a numerical technique as a function of time to simulate the engine operation. The mass balance will have to take into account deposit build-up and the accumulation of evaporation losses. Since these kinetic constants are determined independently from different experiments (they are not fitting constants), there is no guarantee of mathematical convergence under a numerical computational procedure. So if convergence is achieved, it suggests that the constants used are at least internally consistent. This is the basic concept. In this chemical kinetic model, wear and wear debris interaction with lubricants are not taken into account.

3. The nature of the chemical reactions To implement the concept, we need to understand the nature of the chemical interactions occurring in an operating diesel engine and the environments, which influence the reaction rates. The lubricant itself consists of numerous molecular species in base oils and additives. They are very different in structure and therefore will react in different reaction pathways in response to a set of temperature and catalysts. Fortunately, all hydrocarbons oxidize via the free-radical mechanism and the degradation products from different lubricants are remarkably similar [3]. The detailed mechanisms and the rates are of course different for different molecules. Many processes important in diesel engine lubrication such as lubricant–metal interactions, fuel–lubricant interactions, and soot particle–lubricant interactions are not well understood and therefore cannot be reasonably described in mathematical terms. These interactions or the key effects then have to be simulated in the bench tests so that the kinetic constants obtained will include such effects. The key reactions occurring in an engine are: evaporation, thermal degradation, oxidation, oxidative volatility, polymerization, and deposit formation. Evaporative loss can come from several sources: vaporization due to high vapor pressure at high temperatures; thermal decomposition of the oil into smaller molecules hence higher vapor pressure; oxidation of molecules producing small molecules and fragments. Since lubricant molecules are a collection of different molecular-weight fractions, the response to temperature rise in terms of volatility is not linear, i.e., when the heat goes above certain temperature, the volatility increases rapidly. The general oxidation mechanism for hydrocarbons is via a free-radical oxidation mechanism and can be represented by simple equations as shown in figure 1. This includes four reaction steps: initiation, propagation, branching, and termination. The primary


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Figure 2. High-molecular-weight products as measured by gel permeation chromatography under micro-oxidation test conditions.

Figure 1. Oxidation and polymerization reaction mechanisms.

oxidation products such as alcohols, aldehydes, ketones, and acids, in the presence of iron and copper will condense to form high-molecular-weight products. This can be demonstrated by the test results from a micro-oxidation test in figure 2. The oil in a thin film on a steel surface is oxidized at 225 C oxygen, and the reaction products are then analyzed by Gel Permeation Chromatography. Figure 2 shows the progressive increase in molecular weight as a function of time. The polymerization reaction to form high-molecular-weight products has been determined largely from condensation reactions as proposed by Klaus and coworkers [4] (figure 1). Diesel deposit formation is primarily from high-temperature oxidation under thin-film metal-catalysed reacting conditions but the rate can be influenced by the presence of fuel, acids, soot, and combustion conditions as described by Hsu [5] (figure 3).

4. Formulation of the kinetic model A detailed description of the reaction kinetics of such a complex mixture reacting under a wide range of reacting conditions is not possible. Simplification is required. Instead of treating individual species formation as a basis of reaction kinetic equation description, a broad class of reaction products can be used. Such a reaction model has been proposed by Naidu in 1986 [2] and is shown in figure 4. The lubricant ðRHÞ evaporates (k4 ) and reacts with oxygen (k1 ) to form the primary oxidation products ðQÞ. The oxidized products also evaporate and further oxidize to form high-molecularweight products ðPÞ, which eventually form deposits ðDÞ. The extent of reactions is determined by the relative magnitudes of the rate constants (k’s). Therefore, rate equations that describe the reaction system can be derived and are shown in figure 4. When the rate constants can be independently determined, the resulting partial differential equations (with respect to time) can be solved numerically to provide the amount of each component at a given engine simulation point in time.

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Figure 4. The simplified chemical reactions and the kinetic rate equations.

Figure 3. Schematic diagram of diesel deposit formation mechanism. Table 1 List of rate constants.

5. Determination of the kinetic constants A detailed description of how each kinetic constant is determined and the test procedures used to determine them are described in part 11 of this paper and will not be presented here. Briefly, oxidation kinetic constants are determined by a high-pressure Differential Scanning Calorimetry method [6]. The volatility is determined by a Thermogravimetric (TGA) method under Argon (evaporation) and Oxygen atmosphere (oxidative volatility) [7]. The high-molecular-weight products and the deposits are determined by the micro-oxidation technique [8]. Table 1 lists the rate constants determined experimentally for the five lubricants that we have engine test data on.

6. Calculation procedure The number of reactors in the system is determined by the engine design and usually matches the number of critical regions in the engine. Each region will define a

Oil Temperature

240 C

CT5113 250 C

k1 k2 k3 k4 k5 k6 k7 k8

0.09 1.5 0.1 0.0052 0.9 0.05 0.0011 0.088

0.14 2.4 0.154 0.0095 1.5 0.11 0.002 0.14

240 C

CT5126 250 C

0.058 2.0 0.05 0.0025 1.9 0.0375 0.001 0.05

0.1 2.9 0.1 0.0052 2.1 0.075 0.002 0.08

Oil Temperature

CT5213 220 C 245 C

CT5214 220 C 245 C

CT5215 220 C 245 C

k1 k2 k3 k4 k5 k6 k7 k8

0.08 3 0.1 0.0016 1.4 0.001 0.0028 0.13

0.12 6 0.35 0.0136 1.0 0.15 0.005 0.105

0.07 4.5 0.095 0.0115 2 0.0083 0.0035 0.39

All ks are in min1 .

0.16 4.8 0.154 0.006 2.0 0.014 0.006 0.56

0.24 9 0.5 0.028 1.3 0.25 0.01 0.42

0.18 6.8 0.17 0.023 2.5 0.038 0.00726 1.8


Figure 5. A schematic diagram of the engine as represented by the three reactors in series.

set of environmental conditions for that reactor. The reactor is defined by the capacity of the reactor, the temperature, and the residence time. These characteristics of reactors are determined by the dimension of the engine and the actual operating conditions. The physical properties of the oils, such as viscosity, may also affect the capacity of the cylinder liner/piston ring interface (reactor) through variation in oil-film thickness. When the characteristics of a reactor and the lubricant are defined, numerical simulation can be used to calculate the reaction products for a reactor as a function of time based on the kinetic equations. Other aspects of the engine operation such as oil flow rates among the reactors and the degree of mixing between reactants and products in each reactor must also be taken into account. Three reactors are used to represent the engine operation: the cylinder liner/piston ring interface (reactor 1), the top ring groove and the volume above the ring (reactor 2), and the oil sump (reactor 3), as shown in figure 5. In reactor 1, the average temperature per stroke cycle is very high (250–300 C) but the oxygen supply is usually limited due to combustion in the cylinder and the need for oxygen to diffuse into the oil film. Evaporation here is signifiant. In reactor 2, the residence time of the oil is much longer and the temperature is high (lower than reactor 1). With abundant oxygen, oxidative degradation reactions are rapid and deposits will accumulate. In the sump, the temperature is relatively low. The initiation step of oxidation is not likely to take place here. However, with the free radical generated in the ring zone, a significant amount of sludge can form in the sump. The capacity (m), the average reaction temperature (T ), and the residence times (tresd ) of each reactor are determined by specific engine designs. The concentration of a species C(t) at any time (t) is determined by the kinetics of the reactions.

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The oil-flow path is divided into two separate loops. Reactor 1 and reactor 2 constitute one loop. Reactor 2 and reactor 3 constitute another loop. This is to simulate the engine situation. The oil is first pumped from the oil sump (reactor 3) to the top piston ring zone (reactor 2), where the oil resides for several minutes. During this time, the oil circulates between the ring zone (reactor 2) and the cylinder liner/piston ring interface (reactor 1) continuously as the piston goes up and down. When the residence time of the oil in the ring zone (reactor 2) is reached, the oil leaves the ring zone and flows back to the sump (reactor 3). Each time the lubricant leaves a reactor, mass balance among the three reactors is performed to account for the evaporation and deposit accumulation if any. The reacted lubricant then becomes the feed to another reactor and undergoes further reactions. The oil transport between reactors is governed by the residence times in each reactor. The amount of oil exchanged will be determined by the oil pumping rate and mass balance under steady-state operation. Perfect mixing in each reactor is assumed after oil exchange. The change in physical properties of the lubricant can be accommodated each time the mass balance is performed. In the results discussed in this paper, the viscosity is assumed to be constant in calculating the oil-film thickness in reactor 1 throughout the simulation.

7. Obtaining engine parameters The model needs engine parameters such as volume of each reactor, temperature of each reactor, and residence time in each reactor. Some of these parameters can be obtained directly from the design such as the dimensions of the sump, the oil pump rate, and the ring zone gap volume. Some parameters such as the temperature and pressure may need estimation or measurement. To validate the simulation procedure, oils used in the Caterpillar 1K engine dynamometer test conducted at Caterpillar were received in ‘‘double-blind’’ fashion for examination. Therefore, the engine parameters associated with the 1K test configuration were used for the simulation. The kinetic model and the computer program, however, are not specific to 1K test configuration and procedure. The 1K test procedure and conditions are shown in table 2. The engine used is a Caterpillar

Table 2 Caterpillar 1 K engine dynamometer test conditions. Engine Fuel Speed, rpm Load, kW Oil sump temp., C Max. oil ring temp., C Test time, hr

Caterpillar 1Y540 single-cylinder engine Howell 0.4% sulfur diesel test fuel 2100 52 107 330 252

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1Y540 single-cylinder engine fueled by Howell’s 0.4% sulfur diesel test fuel. The various simulation parameters are presented in table 3. The time step used in the computer simulation is 0.05 minutes/step. Much finer time steps were initially used but the computation time became very long without much improvement in simulation results. The volume of the reactor is the volume of lubricant that resides in a particular zone. The volume of the lubricant in a particular region can be estimated by the hardware dimensions and actual measured volumes. For the liner-piston ring interface (top ring), it is estimated using elasto-hydrodynamic (EHD) film-thickness calculation. The temperatures of the reactors are mostly determined by the operating conditions and are either measured or specified in the design. The residence time in a reactor is also determined by the design specification such as speed and size. However, the exact relationship between the residence time and the engine specification is not clear. Estimation or experimental results are necessary for choosing these values. In this case, the experimental observation by Fox [1] has been very useful. The influence of the engine materials is incorporated into k’s through the bench tests. In these tests, steel pans (DSC) and iron pellets (micro-oxidation test) are used to simulate the catalytic effect of iron present in the engine. Figure 6. Flow chart of the computer simulation program.

8. Numerical technique In a real engine operation, the piston movement, the reactor temperatures and the volumes of the reactors are all changing as a function of driving conditions and load. Since we do not have the equation of variation for these variables, it is not feasible to formulate a transient model. Steady-state approximation is used. For simulation purposes, the reactors are assumed to be independent of each other, i.e., there is no interaction between reactors. A mass balance is performed after each cycle between two reactors; the concentrations of the reacted and unreacted materials between reactors are averaged to obtain the new concentrations for the next reaction cycle. Figure 6 shows the computer program flow chart. This procedure is used to calculate the amount of original oil, polymer, deposit, and evaporation at any moment in each reactor. Due to the complexity of the equations, a discrete approximation is used to simulate

Table 3 Engine simulation parameter for Caterpillar 1 K engine.

Capacity, gm Residence time, min. Temperature, C

Reactor 1

Reactor 2

Reactor 3

2 1.2 300

1.5 3.0 280

5000 2500 107

the engine operation. A time step based on the engine speed is chosen. For a four-stroke Caterpillar 1K engine running at 2100 rpm, the time per cycle is 1/1050 min. The time for one cycle will be used as the basic step in advancing the time for the calculation. For reactor 1 and 2 (piston ring/liner interface and the top ring groove), they are coupled for calculation. Oil is pumped to reactor 2 and then reactor 2 interacts with reactor 1 simulating oil goes into the combustion chamber and oxidizes. This interaction stops when the residence time of oil in reactor 2 (ring groove) is reached. For the oil used in this study, an average residence time of about 3 min is used as the residence time of oil in the top ring groove zone. Severe oxidation occurs when the oil is pumped into the combustion chamber to form the liner/piston ring interface which is a function of the piston stroke frequency. Therefore each cycle of the piston constitutes a time step of 1/1050 min. The concentration of every species in the reactors after each time step will be calculated based on the rate equations and the initial species concentrations. After each calculation step, the concentrations in these two reactors are averaged to resemble the oil transport between these two reactors. The size of reactor 2 is assumed to be constant since there is constant replenishment from reactor 3. The evaporation lost during each step is assumed to be

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accumulated in reactor 1. The size of reactor 1 is adjusted after each step. A reaction-time counter was set up to monitor the residence time of oil in reactor 2. After each time step, the reaction-time counter for reactor 2 was increased by 1/1050 min. When the reaction time in reactor 2 equated to its residence time, the concentrations in all three reactors were averaged. The purpose of this averaging process was to take into account of the oil exchange between reactors 2 and 3. This process was repeated until the total test time was reached. The oil consumption is calculated based on the amount of oil evaporated during each time step at the temperature the oil is exposed to. The chemical model only accounts for evaporation and oxidative evaporation effects and does not take into account of leakage via the valve stems or other mechanical mechanisms. The amount of oil evaporated is calculated by the amount of volatile species generated according to the reaction pathway and mass balance. The top groove fill is determined by the percentage of deposit in the second reactor. When the top groove fill is higher than 75%, the oil consumption will be assumed to be four times the normal evaporation rate. The additional oil consumption is taken directly from reactor 3 (the sump) without changing the concentration of the other reactors. According to the 1K test procedure, oil is added to the sump every 12 hours to make up for the loss. The calculation procedure takes this into account by adding fresh oil to reactor 3 and averages the concentration of reacted and unreacted species every 12 h. When the simulation is concluded, the total amount of oil evaporated will be the oil consumption. The concentration of the deposit (D) was used to represent the deposit level.

9. Results and discussion Five oils with engine test data are used for validating the model. CT5113 and CT5126 are two experimental formulations for high-temperature engines. CT5213, CT5214, and CT5215 are reference oils for the 1 K engine test. Values shown for the engine test results are Weighted Total Demerit (WDK), Top Groove Fill (TGF), and Oil Consumption in term of g/kW h. Rate constants (min1 ) for these oils at two temperatures are listed in table 1. A detailed procedure for determining the rate constants will be presented elsewhere. Using these rate constants, results of the simulation are compared with actual 1K engine test data. This is shown in table 4. The simulation results agree well with the engine test results. The CT5126 oil result in the engine test is a special case. The test was terminated early because of excessive oil consumption. The high TGF value indicates that the top ring groove region is filled with deposit, which inhibits the free rotation of the ring pack. After con-

Table 4 Comparison of engine test and the simulation. Lubricant

CT5113

CT5126

CT5213

CT5214

CT5215

252

125

252

252

252

526 50%

577 100%

214 10%

242 50%

328 24%

0.48

3.84

a*

a*

a*

42%

85%

8%

60%

25%

0.42

3.69

0.31

0.5

0.5

Test time, hr

Engine test results WDK TGF Oil consumption, (g/W h) Simulation results TGF Oil consumption, (g/kW h)

a*: The actual oil-consumption data associated with this specific test is not available but these oils have a typical value of 0:5 0:1 g/kWh.

sultation with engine manufacturers regarding this issue, a consensus was reached that it might be reasonable to set a threshold deposit level beyond which the ring pack was not free to rotate. Without taking into account this effect, the oil-consumption rate from simulation is about 0.4 g/kW h. A threshold of 75% TGF is chosen to define the incipient of the lost of ring pack sealing. Whenever the TGF reaches 75%, additional oil lost (set to three times the volatility rate) was used in the simulation model to account for this. With this modification the oil consumption of CT5126 went up to 3.69 g/kW h. The final TGF value of CT5126 from simulation is about 15% lower than the engine test. This may be caused by the assumption that reactor 2 (top groove region) gets sufficient oil supply from reactor 3 (the sump). When most of the top groove is full with deposit, it is likely that blockage of the deposit prevents oil from reaching part of the reactor. This may cause higher temperature in reactor 2 and hence increase the degradation rate. Future modification to take into account this effect may bring the TGF value of the simulation closer to the engine test result.

10. Conclusions A chemical kinetic model and a computer simulation program were successfully combined to predict lubricant performance in a diesel engine test. The kinetic model uses reaction-rate constants determined from special bench tests. A finite-difference computer program simulates the engine operation, and the kinetic model was used to interact with the engine input variables. Results from the simulation agree with the actual Caterpillar 1K engine dynamometer test results.

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Acknowledgement The authors gratefully acknowledge financial support from the Caterpillar Co.

References [1] M.F. Fox, C.J. Jones, D. Hickford, D.J. Picken, F. Kelley and D.E. Copp, Proceedings of Annual Automotive Technology Development Contractors Coordinating Meeting, Dearborn, Michigan, Oct. 24-27, 1994, SAE SP-289, published by SAE, ISBN 1-56091-654-0, 1995. [2] S.K. Naidu, E.E. Klaus and J.L. Duda, Ind. Eng. Chem. Prod. Res. Dev. 25 (1986) 596-603.

[3] S.M. Hsu, C.S. Ku and P.T. Pei, in Aspects of Lubricant Oxidation ASTM STP 916, eds W.H. Stadtmiller and A.M. Smith (American Society for Testing and Materials, Philadelphia, 1986) p. 27. [4] F.E. Lockwood, E.E. Klaus and J.L. Duda, ASLE Trans., 24(2) (1981) 276-284. [5] S.M. Hsu, NBS SP 584, proc. Joint Conf. On Measurements and Standards for Recycled Oil/Systems Performance and Durability (1980) 191. [6] Y. Zhang, P. Pei, J.M. Perez and S.M. Hsu, Lubr. Eng. 48, 3, (1992) 189-195. [7] S.M. Hsu and A.L. Cummings, SAE paper #831682 in SAE SP 558 ‘Lubricant and Additive Effects on Engine Wear’ 51 (1983). [8] J.M. Perez, P. Pei, Y. Zhang and S.M. Hsu, SAE Technical paper #910750, presented at the International Congress and Exposition, Detroit, MI, Feb. 25-March 1, 1991 (Society of Automotive Engineers, Warrendale, PA, 1991).