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Oil transport from scraper ring step to liner at low engine speeds and effect of dimensions of scraper ring step.

INTRODUCTION

In modern gasoline engines, a scraper ring with a step recessed from the lower outer edge has become a common design for the second ring in a piston-ring pack. The step can be either a rectangular cut or a hook-shaped undercut. The latter design is usually called a "Napier ring". A chamfer on the top of a piston third land effectively enlarges the volume of a scraper ring step. The chamfer will be considered as an integrated part of a scraper ring step in this work, unless specially indicated.

Although previous study suggested that a scraper ring step can provide a reservoir for oil [1], the effect of its geometry and dimensions on oil transport and oil consumption has not been completely understood. Dimensions of a scraper ring step are still design options to improve oil consumption performance of gasoline engines. A good understanding of their effects on oil transport can help rationalize the design decisions and reduce the number of design iterations. It also potentially introduces more considerations to the standards of scraper ring design, for instance, the ISO 6623 standard [2].

In this work, an oil transport mechanism that is closely associated with the dimensions of a scraper ring step will be described. Particularly, at low engine speeds, oil can be trapped in the step of a scraper ring. The trapped oil can possibly be pumped into the second ring groove or released to the liner to increase the local oil film thickness. Both results may increase the oil consumption.

This study was originally motivated by the latter one, that is, oil release to the liner. In literature, oil release from a piston-ring pack to a liner has been termed "bridging" [3, 4]. Previous studies [3, 4, 5, 6, 7] demonstrated that bridging occurs when the inertia of a piston (hereafter called 'body acceleration' to distinguish with the inertia of oil) is sufficiently large to drive oil to the top of a piston land before spreading to the liner. Thus, bridging occurs at high engine speeds, typically above 3000rpm. However, in a recent experimental study by Zanghi [8], bridging was observed at less than 1500rpm, at which the body acceleration is not sufficiently large. Readers are referred to Figure 3-12 in [8] for an evidence of bridging at 1500rpm.

For coherence, an experimental evidence of bridging at 800rpm is shown in Figure 1(c), with generous courtesy of Zanghi. It was taken in a 2D-LIF experiment, which allows an observation of oil distribution through a transparent window in the liner [1, 8], as is shown in Figure 1(a). The design of the test engine is shown in Figure 1(b). There is an undercut in the second ring and a chamfer on the upper edge of the piston third land. Figure 1(c) was taken slightly before the top dead center (TDC). A brighter color indicates more oil, and a darker color indicates less oil. The bright vertical stripes in the vicinity of the piston third land are evidences of bridging. They indicate that oil has been attaching to the liner, which is moving downwards relative to the piston.

In terms of oil consumption, bridging is of significant interest because it can increase oil consumption if occurring before TDC [4]. It introduces additional oil to the liner, and the additional oil supply occurs above an oil control ring. Thus, bridging makes an oil control ring lose control of the oil film thickness on a liner. Since automotive engines mostly operate at low speeds during city driving, low-speed bridging can be closely associated with the overall oil consumption. An in-depth understanding on low-speed bridging potentially contributes to designers' knowledge on oil consumption and lead to better design of a piston ring pack.

In this work, a comprehensive study on low-speed bridging will be presented. Computational simulations will first be demonstrated to reveal the physics behind low-speed bridging. Particularly, oil can be trapped in a scraper ring step and the trapped oil can result in bridging. It is entirely different from the high-speed bridging studied in previous work [3, 4, 5, 6, 7]. Then, a quantitative model on oil trapping and low-speed bridging will be presented. The modeling results implied that oil trapping and low-speed bridging are directly associated with the geometry of a scraper ring step. The effects of a few dimensions of a scraper ring step will be discussed.

COMPUTATIONAL SIMULATIONS

In Figure 1(c), there is a bright horizontal stripe at the bottom of the second ring, indicating considerable amount of oil in the step. Given that body acceleration is not sufficient to drive oil from the third land to supply bridging, the oil in the step is a very probable source of bridging. Though this is not directly evident from the experiment, computational simulations revealed that the oil in the step is indeed the source of low-speed bridging.

In this section, all the simulation results to be shown demonstrate oil transport in a radial cross section like Figure 1(b). They were obtained with an OpenFOAM multiphase solver, interFoam. Piston was taken as the reference frame and liner moves. The unsteady body acceleration, as shown in Figure 2, was incorporated in the solver by Wang [5]. The simulations were two-dimensional, and small clearances were neglected. The results implied that these simplifications would not conceal the essential physics behind oil transport. Each simulation started with an arbitrary oil distribution in a scraper ring step and on a third land. It would be continued until the oil transport reached a revolutionary periodic pattern. Then, the results would be analyzed.

Figure 3 shows the computed oil transport in an identical geometry to the test engine. The red color signifies oil and the blue color signifies gas. The orange arrows on the right boundaries indicate the velocity of the liner, and the black arrows on the left indicate the instantaneous body acceleration. From 75[degrees] to 285[degrees] crank angle, the downward body force obviously drives oil on the piston third land to the bottom. However, it is not able to drain oil from the scraper ring step. After 285[degrees] crank angle, the body acceleration becomes upward. As a result, the oil trapped in the step moves upward. The oil distribution at the top right corner at 360[degrees] crank angle indicates that the trapped oil has reached the liner by TDC. Thus, bridging occurs in this condition. The body acceleration is not sufficient to drive oil on the piston third land to the top by TDC. Thus, at low engine speeds, bridging does not require any oil supply from the piston third land. It entirely results from the trapped oil. This observation can be justified by 2D-LIF experiments.

When the body acceleration is downward, the surface of the trapped oil appears "pinned" at the lower edge of the scraper ring step. This is because the tangent line of the solid surface is ambiguous at the sharp edge. As a result, the contact angle between the oil-gas interface and the solid surface is not well defined. When the body force drives oil in the step downward, it would first increase the angle formed by the oil-gas interface and the vertical inner solid surface before draining oil to the piston third land. Thus, oil can be trapped in the scraper ring step.

While the pinning effect can prevent oil from escaping a step, there must be an upward force to balance the downward body force in the bulk of the trapped oil. Figure 3 also shows the pressure distribution in the trapped oil at BDC. The white curve signifies the oil-gas interface, and the colors signify pressure. The pressure fields are approximately hydrostatic in the trapped oil. This is caused by surface tension. Wherever there is a curvature in the oil-gas interface, surface tension will generate a pressure difference in the oil and in the gas. If the gas pressure is approximately constant, a roughly linear variation in the interface curvature can result in a hydrostatic pressure field, which balances the downward body force.

In another type of configuration where the chamfer on the top of a piston third land is smaller or conforms to the step on the scraper ring, similar oil transport was observed. Figure 4 shows the computed oil transport at 800rpm with a rectangular scraper ring step and a conforming third land chamfer. With this design, the oil surface is pinned at the outer edge of the third land chamfer. As a result, oil is trapped in the step. However, in this simulation, the oil supplied to the scraper ring step was not sufficient to arise bridging.

If more oil is supplied to a scraper ring step, the oil can overcome the pinning effect at the edge and be drained to the piston third land by BDC, as is shown in Figure 5. However, the sharp edge significantly restricts the thickness of the oil passage near it. As a result, the draining rate is limited and oil is still effectively trapped. With this increased oil supply to the scraper ring step, bridging occurs.

Figure 4 and Figure 5 both show the pressure distribution in the trapped oil at BDC. Hydrostatic pressure distributions are still present, except for minor gas bubbles.

Computational simulations revealed that oil can be trapped in a scraper ring step at an engine speed as low as 800rpm. It results from the sharp edge of a scraper ring step and the balance between surface tension and downward body acceleration. The trapped oil can result in bridging all by itself, though not necessary.

In contrast, oil trapping is not substantial at higher engine speeds. Figure 6 shows the oil distribution at 135[degrees] crank angle at 2500 rpm with the same scraper ring step. Only a slight quantity of oil can stick to the solid surface of a scraper ring step. It actually results from the viscous effect instead of surface tension, which can be supported by the modelling results to be shown. It indicates that oil trapping is evident only when body acceleration is sufficiently weak so that surface tension is able to balance it.

MODELING

In this section, a theoretical modeling of oil trapping and low-speed bridging will be demonstrated. The formulation will be presented with the trapping model only. The same formulation can be applied to the low-speed bridging model.

Oil Trapping

Critical Speed for Oil Trapping

Simulations indicated that significant quantity of oil can be trapped at low speeds, while only a slight quantity of oil sticks to a scraper ring step at high speeds. One can therefore expect a critical engine speed, which is the maximum speed at which significant quantity of oil can be trapped and the minimum speed at which oil can hardly be trapped. A theoretical model was developed in order to evaluate this critical speed.

If the critical speed is less than the idle speed of an engine, oil trapping can be avoided in engine operations. Thus, approaches to reducing the critical speed are expected from the modeling.

A practical definition of the critical speed can be vague, since no oil can reside in a scraper ring step at no speed. In the model to be demonstrated, the critical speed for oil trapping is defined as the maximum speed at which a continuous oil-gas interface connecting the bottom edge and the upper surface of a scraper ring step can be maintained. An example of oil trapping is illustrated in Figure 7(a). In contrast, if an oil surface breaks up as shown in Figure 7(b), simulations indicated that the quantity of "trapped" oil would be very small and is usually insufficient to support low-speed bridging. Thus, the latter case would not be considered as oil trapping in the model.

As implied in the foregoing section, the chamfer on the top of a piston third land may conform to the step of the scraper ring (Figure 8(a)), be smaller than the step (Figure 8(b)), or be larger than the step (Figure 8(c)). Although the experimental results were obtained with the third configuration, the development of the model will be demonstrated with the first two. The same modeling approach can be applied to the third configuration. It turned out that the critical speed with the third design is generally larger. Furthermore, the wedge labeled by the shaded region in Figure 8(c) constitutes an oil reservoir for the second ring groove, which could possibly increase oil consumption.

Formulations

Computational simulations indicated that the primary force balance in trapped oil is between surface tension and body acceleration. Mathematically, it is described by the Young Laplace Equation:

[p.sub.0] = [rho]ax = [sigma] x -[h.sub.xx]/[(1 + [h.sub.x.sup.2]).sup.2/3]. (1)

The coordinate system is shown in Figure 9(b). In Eq. (1). x is the vertical coordinate, h is the coordinate of oil surface, [p.sub.0] is oil pressure at x = 0, [rho] is oil density, a is body acceleration, and [sigma] is surface tension of oil-gas interface. Subscript x denotes derivative with respect to x. Here, [p.sub.0] is an unknown variable to be solved for.

If oil can be trapped at an engine speed, surface tension must be able to balance the maximum downward body acceleration at that speed. Therefore, a is taken as the maximum downward body acceleration at a certain speed. Note that the maximum body acceleration does not occur at the BDC, though the difference is small and cannot be recognized in Figure 2.

The boundary conditions at the bottom of an oil surface are:

[h.sub.x](x = 0) = -cot [alpha] (2)

h(x = 0) = c (3)

where c is the depth of a scraper ring step, [alpha] is the maximum "contact angle" with which oil will not drop to the piston third land, both defined in Figure 9. Eq. (3) is approximate when there is a thin oil passage near the edge, and exact when the contact line is pinned at the edge. Note that Eq. (2) and (3) only correspond to the limiting case when the quantity of trapped oil reaches the maximum. If the actual oil supply to a scraper ring step is insufficient, the lower contact line may not reach the bottom edge, or the actual "contact angle" may not reach the limit; if the actual oil supply to a scraper ring step is redundant, the redundant fraction of oil will be drained away from the step. An evaluation of the actual oil supply involves a modeling of oil transport in other regions in a piston-ring pack, which is likely to be complicated. By assuming the maximum quantity of trapped oil, the analysis is focused on the scraper ring step and hence simplified. This simplification will not introduce essential uncertainties in the model; in fact, it minimizes the uncertainties. If oil trapping can be avoided in this limiting case, it can be avoided with any actual oil supply.

The restricting conditions on the top of an oil surface depend on the relationship between the tapered angle of a scraper ring step [gamma] and the receding contact angle [psi], both defined in Figure 9.

When [gamma] > [psi], as is illustrated in Figure 10 left, h is a multi-valued function of x. A hydrostatic pressure field requires that the oil-gas interface must be symmetric about a vertical line passing the apex of the interface. Thus, only the interface to the left of the symmetric axis is to be functionalized. The restricting conditions are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

[h.sub.e] + ([h.sub.e] - [h.sub.s]) = w - ([x.sub.s] - d) x cot [gamma] ([psi] < [gamma]) (6)

where d is the height of a scraper ring step, w is the width of the step. both defined in Figure 9(a); [x.sub.e] is the location of the apex, and [x.sub.s] is the location of the upper contact line, both illustrated in Figure 10. Eq. (6) dictates that an oil-gas interface originating from the bottom edge of a scraper ring step can be continuously extended to the upper surface, which is the definition of oil trapping in the model.

When [gamma] [less than or equal to] [psi], h is a single-valued function of x. Restricting conditions on the top is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

[h.sub.s] = w - ([x.sub.s] - d) x cot [gamma] (8)

where [x.sub.s] is the location of the upper contact line, as is illustrated in Figure 10 right. Here, Eq. (8) enforces the definition of oil trapping.

Three dimensionless groups were introduced:

[eta] = x x [square root of ([rho]a/2[sigma])] [xi] = [p.sub.0] x [square root of (2/[rho]a[sigma])] k = d x [square root of ([rho]a/[sigma])] (9)

By integrating Eq. (1) with boundary condition (2), one get:

-[h.sub.x]/[(1 + [h.sub.x.sup.2]).sup.1/2] = F([eta]) = -[[eta].sup.2] + [xi][eta] + cos [alpha] (10)

Eq. (10) is the governing equation in the model, and Eq. (3) to (8) serve as boundary/restricting conditions.

After some calculus and algebra, Eq. (8) becomes:

k = [square root of 2] x d/D x B([xi], [gamma], [alpha], [absolute value of ([gamma] - [psi])]) (11)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

[[eta].sub.s] = 1/2 ([xi] + [square root of ([[xi].sup.2] + 4(cos [alpha] + cos ([gamma] - [psi]))]) (13)

[[eta].sub.e] = 1/2 ([xi] + [square root of ([[xi].sup.2] + 4 (cos [alpha] + 1))] (14)

and

D = d + (w - c) tan [gamma] (15)

It is noted that the left hand side of Eq. (10) must lie between -1 and 1 for all [eta] [member of] [0, [[eta].sub.e]] when [gamma] > [psi], or all [eta] [member of] [0, [[eta].sub.s]] when [gamma] [less than or equal to] [psi]. It requires that:

[xi] [less than or equal to] 2 [square root of (1 - cos [alpha])] (16)

With this limitation on [xi], the function B has a maximum, denoted with [B.sub.max] hereafter. Eq. (11) requires that:

a [less than or equal to] 2[sigma]/[rho][D.sup.2] x [B.sub.max.sup.2] ([gamma], [alpha], [absolute value of ([gamma] - [psi])]) (17)

Eq. (17) gives a maximum body acceleration. When a is larger than this maximum, there is no valid solution satisfying Eq. (6) or Eq. (8). That is, a continuous interface connecting the bottom and the top does not exist and oil cannot be trapped. From a more physical perspective, when the body acceleration is too large, surface tension will not be able to balance the large hydrostatic pressure gradient in the trapped oil. Since body acceleration is proportional to the square of engine speed, Eq. (17) specifies a maximum engine speed.

Figure 11 and Figure 12 shows the images of the function [B.sub.max].

A valid k value can be plugged into Eq. (11) to numerically solve for [xi], as a function of [gamma], [alpha], and [psi]. The oil-gas interface profile could then be obtained by numerical integration of Eq. (10). Figure 13 shows a set of oil-gas interfaces at different engine speeds. The maximum speed specified by Eq. (17) is 921rpm in this design. Generally, the oil-gas interface moves towards the inner solid surface as engine speed increases, except for a very small range of speeds near the maximum speed. In engine operations, the downward body acceleration increases gradually and the oil-gas interface should move inwards gradually. Thus, the solutions to the left of the oil-gas interface at 921rpm are considered improper in this application. The fact that the oil-gas interface moves towards the inner solid surface as body acceleration increases coincided with computational simulations.

It is possible that the oil surface at the maximum engine speed, as is specified by Eq. (17), intersects with the inner solid surface of a scraper ring step. To ensure that this does not occur, the oil surface under a set of valid k values would be solved for. The maximum speed at which the oil surface does not intersect with the inner solid surface was evaluated by interpolation. This speed is the critical speed for oil trapping. It is no larger than the maximum speed specified by Eq. (17).

Indications of the Model

The model indicates that the critical speed for oil trapping depends on two effects:

1. Whether surface tension is able to balance the hydrostatic pressure gradient;

2. Whether an oil surface intersects with the inner solid surface of a scraper ring step.

The first effect will be called the primary effect in the following discussions, and the second one will be called the secondary effect.

Primary Effects

Eq. (17) indicates that the primary effects depend on four categories of parameters:

1. Engine configuration: crank radius and length of connecting rod. They come into effect through the body acceleration;

2. Oil properties: density [rho], and surface tension of oil-gas interface [sigma];

3. Contact angles between oil-gas interface and solid surfaces: [alpha] and [psi] as defined in Figure 9(b);

4. Geometry of a scraper ring step: an integrated length parameter D, and the tapered angle of a step [gamma]. Note that the parameter D has a geometric indication. As illustrated in Figure 14, it is the height of a scraper ring step measured along the extension of the piston third land.

The first category of parameters is usually based on other considerations other than piston ring design. It will not be discussed in this work.

In practice, density and surface tension of engine oils does not vary significantly at typical engine operating temperatures. Furthermore, it is difficult to significantly change these properties by oil formulation. Anyway, Eq. (17) clearly indicates that the critical speed due to the primary effects is proportional to [([sigma]/[rho]).sup.1/2]. Therefore, the effect of oil properties will not be further discussed.

The choice of the limiting angle [alpha] can be artificial. The receding contact angle y may not be easily measured and may vary with time. Fortunately, as shown in Figure 11 and Figure 12, the critical speed is not sensitive to the two contact angles. Therefore, [alpha] and [psi] will be treated as two constants in the model. It is suggested that [alpha] = 90[degrees] and [psi] = 0[degrees]. These choices are based on the fact that surface tension of oil is small and oil tends to wet a solid surface. Moreover, the choice of [alpha] = 90[degrees] was strongly supported by the computational simulations.

A significant indication of the model is that the critical speed for oil trapping can be effectively modified by the geometric design of a scraper ring step. Although the model takes all the forgoing parameters as input, the effects of geometric design will be the focus of this work.

Secondary Effects

By intersecting with an oil-gas interface, the inner solid surface of a scraper ring step possibly gives rise to a further reduction to the critical speed. The reduction can be modified through the geometric design of the inner solid surface of a scraper ring step,

Modeling results and the effect of each geometric parameter are to be presented in the section "Results and Discussions".

Low-Speed Bridging

The same formulation can be applied to evaluate the quasi-static oil-gas interface profile under the maximum upward body force. In this way, the range of engine speeds at which low-speed bridging occurs can be predicted. There are two approaches to predict it:

1. Given the quantity of trapped oil, the location of the upper contact line of the trapped oil at TDC can be calculated. If it exceeds the liner, low-speed bridging occurs; otherwise, low-speed bridging does not occur;

2. The upper contact line is fixed at the intersection of a scraper ring step and a liner. Then, the volume of oil at TDC can be calculated. If the actual quantity of trapped oil exceeds it, low-speed bridging occurs; otherwise, low-speed bridging does not occur.

In most cases, the results given by the two approaches coincided with each other.

There are two important uncertainties in the model of low-speed bridging. First, the bridging model requires the quantity of trapped oil as an input. However, it is dependent of the oil supply to a scraper ring step, which may depend on complicated oil transport mechanisms. A simple approach is to utilize the maximum quantity of oil that can be trapped, which can be predicted with the trapping model. However, in this way, only the risk of bridging is evaluated.

Second, unlike the trapping model, the bridging model is sometimes sensitive to the advancing contact angle [phi], as is defined in Figure 15. With a smaller contact angle [phi], oil is more likely to wet the solid surface of a scraper ring step. Therefore, oil is more likely to reach the liner and arise bridging.

Hence, the results of the low-speed bridging model contain more uncertainties than the trapping model.

ELIMINATION OF LOW-SPEED BRIDGING

There are two approaches to eliminate low-speed bridging:

1. To allow oil trapping, but avoid low-speed bridging when there is oil trapped. That is, to make the critical speed for low-speed bridging less than the critical speed for trapping;

2. To completely avoid oil trapping in engine operations. That is, to make the critical speed for trapping less than the idle speed.

The first approach would largely depend on a reliable model on low-speed bridging. However, as explained, the low-speed model contains significant uncertainties.

A more significant concern with the first approach is the low-speed bridging in transient conditions. An example is illustrated in Figure 16. The solid curve shows the maximum quantity of trapped oil, which was obtained with the trapping model. The dashed curve shows the minimum quantity of oil that is capable of arising bridging, which was obtained with the low-speed bridging model. At slightly more than 900 rpm, the latter is greater than the former, indicating that low-speed bridging can be avoided. However, this is true only when the engine operates steadily at a constant speed. Suppose an engine initially operates at 700rpm and the quantity of trapped oil is 0.3[mm.sup.2] per width. This condition is labeled "A" in Figure 16. All oil can be trapped but bridging does not occur. If the engine suddenly accelerates to 910rpm, the quantity of trapped oil will not vary immediately. Thus, the operating condition moves horizontally to the point B in Figure 16. At this time, the quantity of trapped oil exceeds both the trapping capability and the bridging requirement. If the body force is downward at this moment, some oil can be drained to the piston third land. However, if the body force is upward, bridging will occur. Although low-speed bridging can be avoided in a steady condition at 910rpm, there is no guarantee that it can be avoided in a transient condition. As long as there is oil trapped in a scraper ring step, low-speed bridging possibly occurs. And the performance of oil can be unpredictable.

On the other hand, if oil trapping can be completely avoided, not only low-speed bridging can be suppressed in all conditions, but also oil supply to the second ring groove can be decreased. Therefore, the second strategy, which is to completely avoid oil trapping, is a more fundamental approach to eliminate low-speed bridging.

RESULTS AND DISCUSSIONS

In this section, the critical speeds predicted by the trapping model will be shown. The geometric parameters that can significantly reduce the critical speed will be identified.

In the results to be presented, engine configurations are: con-rod length = 0.158m, crank radius = 0.044m; oil properties are: density = 800kg/[m.sup.3], surface tension = 0.02N/m; contact angles are: [psi] = 0[degrees] and [alpha] = 90[degrees].

Primary Effects

Eq. (17) indicates that the primary effects depend on only two geometric parameters: D and [gamma]. There effects are separable.

Clearly, the maximum speed determined by Eq. (17) is inverse proportional to D. However, as indicated in Eq. (15), D depends on the clearance between a piston third land and a liner (w-c). It is not for certain whether a designer of scraper ring has discretion of this clearance. Therefore, for the ease of ring designers, the height measured along a liner (d) will be discussed instead of the height

measured along the extension of a third land (D).

Figure 17 shows how the critical speed varies with the height of a scraper ring step (d). Only the primary effect is considered here. The critical speed substantially decreases with the height d. A larger value of d gives a larger value of D, and thus a smaller critical speed. Physically, with a larger height of a scraper ring step, surface tension must balance a larger hydrostatic pressure difference at a same engine speed. As a result, an oil-gas interface breaks up at a lower engine speed.

Figure 18 shows how the critical speed varies with the tapered angle of a scraper ring step ([gamma]). Only the primary effect is considered here. The critical speed remarkably decreases with [gamma]. Here, d, w and c are fixed. Therefore, an increase in [gamma] results in a larger D value. Moreover, the tapered angle [gamma] also affects the critical speed through the function [B.sub.max] in Eq. (17), though this effect is not monotonic and relatively slight. Physically, the latter effect reflects the fact that the tapered angle [gamma] determines how and where an oil-gas interface lands on the upper solid surface of a scraper ring step.

Secondary Effects

The secondary effects possibly introduce further reduction to the critical speed. The reduction is determined by the profile of the inner solid surface, namely, the height of a piston chamfer (s), the angle of a piston chamfer ([theta]), the depth of a scraper ring step (c), and the radius of a rounded corner (R), all defined in Figure 9(a).

Modeling results indicated that the secondary effects reduce the critical speed only when d and/or [gamma] are/is small. When they do reduce the critical speed, the radius of a rounded corner (R) is usually the restricting parameter, suggesting that an oil-gas interface is more likely to intersect with the inner solid surface at the top. The depth of a step (c) is effective when it is small, typically smaller than 0.25mm. The height (s) and the angle ([theta]) of a piston chamfer seldom affect the critical speed.

Figure 19 shows how the critical speed varies with the radius of a rounded corner (R). When R is small, the rounded corner will not intersect with the oil-gas interface, and the critical speed is completely determined by the primary effects. As R increases, the rounded corner is more likely to intersect with the oil-gas interface. As a result, the critical speed reduces. However, the reduction is slight compared to the primary effects.

Figure 20 shows how the critical speed varies with the depth of a scraper ring step (c). When c is large, the inner solid surface of the step will not intersect with the oil-gas interface, and the critical speed is completely determined by the primary effects. As c becomes smaller, the inner solid surface is more likely to intersect with the oil-gas interface. As a result, the critical speed reduces. However, still, the reduction is slight compared to the primary effects.

Modeling results suggested that the secondary effects on the critical speed are limited. Furthermore, an increase in R and/or a decrease in c decrease(s) the volume of a scraper ring step, which potentially compromises its oil storing function.

The Critical Speed

The modeling results indicated that the critical speed for oil trapping primarily depends on whether surface tension is capable of balancing the body acceleration by adjusting the oil-gas interface profile in a scraper ring step. The most effective approaches to reducing the critical speed for oil trapping are:

1. To increase the height of a scraper ring step (d);

2. To increase the tapered angle of a scraper ring step ([gamma]).

Two auxiliary approaches are:

1. To increase the radius of a rounded corner (R);

2. To decrease the depth of a scraper ring step (c).

Alternative approaches to reducing the critical speed were discussed in [9].

REMARKS ON THE MODEL

In the model, the definition of oil trapping is somehow artificial. Above the critical speed predicted by the model, oil can still reside in a scraper ring step. Therefore, the modeling result does not bear any strict meaning in reality. It is a general reference for engine designers.

Furthermore, in the model, only the quasi-static balance between surface tension and body acceleration was addressed. In reality, due to the viscous effect, a continuous oil surface may still be maintained at an engine speed slightly above the modelled critical speed. Therefore, the model possibly underestimates the critical speed for oil trapping.

On the other hand, this model considered the case when the quantity of trapped oil reaches the maximum. The actual oil supply to a scraper ring step can be less than this maximum. Thus, the risk of oil trapping can be exaggerated by this model.

The input data of the model may contain uncertainties. First, oil properties, especially surface tension, may not be readily obtained at an operating temperature of as high as 200[degrees]C. Second, ring dynamics, thermal and mechanical deformations may alter the designed geometry of a scraper ring step.

In the formulation, the gas pressure was assumed uniform. When there is a strong gas flow in the vicinity of a scraper ring step, gas pressure distribution and dynamic forces can bear more significant effects. Hence, the model is more applicable in low-load conditions.

Because of these limitations, it is always advisable to verify a modeling result with engine tests before application. However, despite all the limitations, the modeling results coincided with all the existing experiments, conducted by Zanghi, and computational simulations. For instance, in the experiments conducted by Zanghi, oil trapping and low-speed bridging were observed at 800rpm and 1500rpm, but not at 2500rpm or 3500rpm. It indicated that the critical speed should be greater than 1500rpm and less than 2500rpm. The trapping model predicted a critical speed of 1736rpm, which indeed lies in the range specified by the experiments. A complete comparison is shown in Table 1.

Although the critical speed for oil trapping is not necessarily identical to the critical speed for low-speed bridging, it turned out that an application of the mere trapping model generally suffices to study both oil trapping and low-speed bridging. It implies that these two critical speeds should be generally the same. Thus, it is deemed that the theoretical model for oil trapping can provide a satisfactory reference for engine designers.

CONCLUSION

In this work, the mechanism of low-speed bridging has been identified. It results from the oil trapped in a scraper ring step, and does not require any oil supply from a piston third land. Despite the similar appearance in experiments, low-speed bridging is an entirely different phenomenon from the high-speed bridging studied in [4, 5, 6].

Bridging introduces additional oil supply to a liner, and it is beyond the control of an oil control ring. As a result, bridging can be a possible contributor to oil consumption. Since an automotive engine often operates at low speeds during city driving, an in-depth understanding on low-speed bridging is of significant interest.

It has been suggested that the best approach to eliminating low-speed bridging is to avoid oil trapping. This can be achieved by reducing the critical trapping speed to less than the idle speed. A quasi-static model of oil trapping has been developed based on the primary force balance, which is between surface tension and body acceleration. The modeling results indicate that the critical speed can be effectively reduced by carefully designing the dimensions of a scraper ring step. The two most effective methods are:

1. To increase the height of a scraper ring step;

2. To increase the tapered angle of a scraper ring step.

Two auxiliary methods are:

1. To increase the radius of a rounded corner;

2. To decrease the depth of a scraper ring step.

Despite the limitations of the theoretical model, the modeling results coincided with existing experiments and simulations. Thus, the model can provide valuable references for the designers of a piston-ring pack.

It is worth clarifying that this work was only focused on the elimination of oil trapping through geometric design of a scraper ring step. Another fundamental approach is to restrict the oil supply to a scraper ring step. The latter is beyond the scope of this study.

Through this study, the effects of individual dimensions of a scraper ring step have been better understood. It possibly introduces more considerations to the existing standards of scraper ring design, for instance, the ISO 6623 standard [2].

Tianshi Fang and Tian Tian

Massachusetts Institute of Technology

REFERENCES

[1.] Thirouard, B., "Characterization and modeling of the fundamental aspects of oil transport in the piston ring pack of internal combustion engines," Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 2001.

[2.] ISO (International Organization for Standardization), "Internal combustion engines--Piston rings--Scraper rings made of cast iron," ISO Standard 6623, Jul. 2013.

[3.] Vokac, A. and Tian, T., "An Experimental Study of Oil Transport on the Piston Third Land and the Effects of Piston and Ring Designs," SAE Technical Paper 2004-01-1934, 2004, doi:10.4271/2004-01-1934.

[4.] Przesmitzki, S., Vokac, A., and Tian, T., "An Experimental Study of Oil Transport between the Piston Ring Pack and Cylinder Liner," SAE Technical Paper 2005-01-3823, 2005, doi:10.4271/2005-01-3823.

[5.] Wang, Y., "Air flow effects in the piston ring pack and their implications on oil transport," Master's thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 2012.

[6.] Thirouard, B. and Tian, T., "Oil Transport in the Piston Ring Pack (Part I): Identification and Characterization of the Main Oil Transport Routes and Mechanisms," SAE Technical Paper 2003-01-1952, 2003, doi:10.4271/2003-01-1952.

[7.] Thirouard, B. and Tian, T., "Oil Transport in the Piston Ring Pack (Part II): Zone Analysis and Macro Oil Transport Model," SAE Technical Paper 2003-01-1953, 2003, doi:10.4271/2003-01-1953.

[8.] Zanghi, E. J., "Analysis of Oil Flow Mechanisms in Internal Combustion Engines via High Speed Laser Induced Fluorescence (LIF) Spectroscopy," Master's thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 2014.

[9.] Fang, T., "Computations and modeling of oil transport between piston lands and liner in internal combustion engines," Master's thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 2014.

ACKNOWLEDGEMENTS

This work was sponsored by the Consortium on Lubrication in Internal Combustion Engines with additional support by Argonne National Laboratory and the US Department of Energy. The current consortium members are Daimler, Mahle, MTU, PSA Peugeot Citroen, Renault, Shell, Toyota, Volkswagen, Volvo Cars, Volvo Truck, and Weichai Power. The authors appreciate Eric James Zanghi for the experimental support to this work.

LIST OF SYMBOLS

Oil Properties

[rho]--Density of oil

[sigma]--Surface tension of oil-gas interface

Contact Angles

[alpha]--Limiting angle on outer edge of piston chamfer on top of third land (in trapping model)

[phi]--Advancing contact angle on top surface of scraper ring step (in low-speed bridging model)

[chi]--Receding contact angle on piston chamfer on top of third land (in low-speed bridging model)

[psi]--Receding contact angle on top surface of scraper ring step (in trapping model)

Dimensions of Scraper Ring Step

c--Depth of scraper ring step

d--Height of scraper ring step (along liner)

D--Height of scraper ring step along extension of piston third land

R--Radius of rounded corner of scraper ring step

s--Height of piston chamfer on top of third land

w--Width of scraper ring step

[gamma]--Tapered angle of scraper ring step

[theta]--Angle of piston chamfer on top of third land

Other Parameters

a--Body acceleration (inertial acceleration)

h--Oil surface profile, measured in thickness

[h.sub.e]--h coordinate of apex in oil surface

[h.sub.s]--h coordinate of upper contact line

[p.sub.0]--A reference of oil pressure (oil pressure at x = 0)

x--Coordinate along piston motion

[x.sub.e]--x coordinate of apex in oil surface

[x.sub.s]--x coordinate of upper contact line

Dimensionless Groups

k--Dimensionless engine speed

[eta]--Dimensionless x

[xi]--Dimensionless [p.sub.0]

Table 1. Comparison between modeling results and experiments or
simulations

              Geometry &             Critical   Observation, of oil
              dimensions (in mm or   speed      trapping & low-speed
              [degrees])             for oil    bridging in
                                     trapping   experiments or
                                     by         simulations
                                     modeling

Experiments   Figure 1(b)            1736rpm    Observed at 800rpm and
(by Zanghi)                                     1500rpm;

                                                Not at 2500rpm or
                                                3500rpm.

              Rectangular step       1264rpm    Observed at 800rpm;
              with piston chamfer
              (Figure 4 & Figure
              5)

              d = 0.689,                        Not at 1500rpm,
              [gamma]=0[degrees],               2500rpm, or 4500rpm.
              w = 1, c = 0.5, R =
              0, [theta] =
              30[degrees], s =
              0.289

Simulations   Same rectangular       2266rpm    Observed at 800rpm and
              step without piston               1500rpm;
              chamfer

              d = 0.4, [gamma] =                Not at 2500rpm or
              0[degrees], w = 1, c              4500rpm.
              = 0.5, R = 0,
              [theta] =
              0[degrees], s = 0

              Napier ring with                  Observed at 700rpm;
              piston chamfer

              d = 0.689, [gamma]=    752rpm     Not at 800rpm, 900rpm,
              30[degrees], w = 1,               or 1000rpm.
              c = 0.5, R = 0.2,
              [theta] =
              30[degrees], s =
              0.289
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Author:Fang, Tianshi; Tian, Tian
Publication:SAE International Journal of Fuels and Lubricants
Article Type:Report
Date:Apr 1, 2016
Words:6909
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