Contact-fluid interfacial shear strength and its critical importance in elastohydrodynamic lubrication
The Authors
Y. Zhang, Shanxi Institute of Technology, Taiyuan, People's Republic of China
Abstract
Purpose – To review, analyze and present the effects of the contact-fluid interfacial shear strength and contact-fluid interfacial slippage and the critical importance of these effects in elastohydrodynamic lubrication (EHL).
Design/methodology/approach – The experimental and theoretical research results of the contact-fluid interfacial shear strength and its caused contact-fluid interfacial slippage in hydrodynamic lubrication and especially in EHL obtained in the past decades and progressed in recent years by the present author and by others are reviewed. Analysis and presentation are made on both the contact-fluid interfacial shear strength versus fluid pressure curve for a given bulk fluid temperature in an isothermal EHL and the influence of the bulk fluid temperature on this curve.
Findings – It is very clearly and well understood from the present paper that the value of the contact-fluid interfacial shear strength in the inlet zone in an EHL contact, i.e. at low EHL fluid film pressures is usually low and usually has rather a weak dependence on the EHL fluid film pressure. This proves the correctness of the EHL theories previously developed by the author based on the assumption of this low value and dependence on the EHL fluid film pressure of the contact-fluid interfacial shear strength. It is also very clearly understood that the bulk fluid temperature usually has a strong influence on the value of the contact-fluid interfacial shear strength in EHL and the increase of this temperature usually significantly reduces the value of the contact-fluid interfacial shear strength in EHL.
Practical implications – A very useful material for the engineers who are engaged in the design of EHL on gears, cams and roller bearings, and for the tribology scientists who thrust efforts in studying EHL and mixed EHL both by theoretical modeling and by experiments.
Originality/value – A new and generalized mode of mixed EHL is originally proposed by incorporating the finding of a more realistic mode of the contact regimes in a practical mixed EHL based on the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects. This mode of mixed EHL should become the direction of the theoretical research of mixed EHL in the future.
Article Type:
Viewpoint
Keyword(s):
Lubrication; Shear strength; Tribology.
Journal:
Industrial Lubrication and Tribology
Volume:
58
Number:
1
Year:
2006
pp:
4-14
Copyright ©
Emerald Group Publishing Limited
ISSN:
0036-8792
Nomenclature
C 0 dimensionless contact-fluid interfacial shear strength in the inlet zone of an EHL contact (Zhang, 2004a)
G material parameter of an EHL contact (Zhang, 2004a)
p fluid pressure
p s bulk fluid or contact-fluid interface solidification pressures
R compound curvature radius of an EHL contact (Zhang, 2004a)
S slide-roll ratio of an EHL contact (Zhang, 2004a)
τ l shear strength of the contact surface adhering layer-bulk fluid interface (i.e. maximum endurable shear stress of the contact-fluid interface), bulk fluid shear strength or contact-fluid interfacial shear strength
τ l0 bulk fluid shear strength or maximum endurable shear stress of the contact-fluid interface at ambient pressure
α τl bulk fluid shear strength or maximum endurable shear stress of the contact-fluid interface-pressure proportionality
1 Introduction
Lubricant rheology, contact surface roughness and lubricant film thermal effects are three important topics in both the theoretical and experimental studies of hydrodynamic lubrication. Conventional hydrodynamic lubrication theory has been well established, which was based on the assumptions of Newtonian fluids, ideally smooth contact surfaces and isothermal lubricant films (Pinkus and Sternlicht, 1961). In recent decades, the fluid non-Newtonian, contact surface roughness and lubricant film thermal effects were, respectively, incorporated into the study of hydrodynamic lubrication. These also occurred in the research of elastohydrodynamic lubrication (EHL) in the past. These three important effects in hydrodynamic lubrication and especially in EHL still need to be more thoroughly investigated especially in severe operating conditions, i.e. for heavy loads, high rolling speeds, large slide-roll ratios and high bulk fluid temperatures. The developments of the theories of these lubrications incorporating these three important effects for severe operating conditions are still in fast progress (Zhang et al., 2001a, b, 2000).
Smith (1960) proposed the concept of fluid shear strength to explain the traction in EHL. The fluid shear strength was later further experimentally identified as a fundamental fluid property by Paul and Cameron (1979), Evans and Johnson (1986), Bair and Winer (1992), and Feng and Ramesh (1993). At high pressures, the fluid shear strength was found by them to typically satisfy the following equation: Equation 1 where τ l0 is the fluid shear strength at ambient pressure extrapolated from the fluid shear strengths at high pressures, α τl is the fluid shear strength-pressure proportionality and p is the pressure of the fluid. The theoretical studies of EHL based on the non-Newtonian fluid model incorporating the fluid shear strength predicted by equation (1) were later plentifully made (Gecim and Winer, 1980; Shieh and Hamrock, 1991). However, it was typically shown by those studies that the fluid shear strength effect on EHL film thickness is modest even in severe operating conditions. In those studies, the contact-fluid interfacial slippage was not considered and the EHL film thickness percentage reduction was 40 percent to the most extent in severe operating conditions due to the fluid shear strength effect (Gecim and Winer, 1980). Later, Jacobson and Hamrock (1984) analytically studied the effects of the fluid shear strength predicted by equation (1) on both EHL film pressure and EHL film thickness by incorporating the contact-fluid interfacial slippage caused by the fluid shear strength effect. However, the slide-roll ratios used by them were no more than 0.1 and their results for those slide-roll ratios showed that the fluid shear strength effects on both EHL film pressure and EHL film thickness were rather limited. It was pointed out by Zhang et al. (2002a) that it is inadequate to neglect the contact-fluid interfacial slippage effect in the analysis of EHL when the fluid shear strength is incorporated. It was also pointed out by them that the physical condition for the presence of the contact-fluid interfacial slippage due to the fluid shear strength effect must be incorporated and satisfied in the analysis of EHL when both the fluid shear strength and the contact-fluid interfacial slippage effects are incorporated. Otherwise, the analytical EHL results based on both the fluid shear strength and the contact-fluid interfacial slippage effects will be wrong and thus misleading. However, the incorporation of this physical condition into an analysis of EHL will substantially enhance the difficulty of obtaining the numerical solution of EHL. This is now still an exacting challenge to the computing man who is trying to obtain the numerical solution of EHL when incorporating both the fluid shear strength and the contact-fluid interfacial slippage effects. This difficulty may also be the reason why Jacobson and Hamrock (1984) were only able to give the results of EHL for the slide-roll ratios lower than 0.1 when incorporating both the fluid shear strength and the contact-fluid interfacial slippage effects, and thus obscured the substantial effect of fluid shear strength on EHL. Those EHL results for low slide-roll ratios obtained by Jacobson and Hamrock (1984) are therefore very inadequate. In the future research of EHL incorporating both the fluid shear strength and the contact-fluid interfacial slippage effects, this difficulty needs to be carefully addressed. In the past, fortunately, Zhang et al. (2002a) had a chance to overcome this difficulty to obtain the typical numerical solution of EHL for the slide-roll ratios varying from 0 to 2.06 for medium load and rolling speed when both the fluid shear strength and the contact-fluid interfacial slippage effects were considered. They analytically showed that the fluid shear strength and contact-fluid interfacial slippage effects on both EHL film pressure and EHL film thickness were very strong for large slide-roll ratios over 1.0 in this operating condition. These effects caused the largely flattened and reduced EHL film pressure profiles and the greatly reduced EHL film thickness especially in the Hertzian contact zone for large slide-roll ratios over 1.0. The fluid shear strength and contact-fluid interfacial slippage effects can therefore be very significant in EHL. One therefore has a correct understanding on these effects from the numerical EHL solutions obtained by Zhang et al. (2002a).
Zhang et al. (2001a) proposed that equation (1) may usually not be able to be used for predicting the shear strength of the fluid at low pressures. They suggested that the extrapolation from equation (1) for the shear strength of the fluid at low pressures (in liquid state) usually give a much higher value than the actual value of this fluid shear strength. Zhang et al. (2001a) proposed that it is critically important to accurately predict the shear strength of the fluid at low pressures (in liquid state), i.e. in EHL inlet zones in the analysis of EHL when both the fluid shear strength and contact-fluid interfacial slippage effects are incorporated, since the fluid behavior in the EHL inlet zone is determinative to EHL film thickness and this fluid behavior is determined by the shear strength of the fluid in the EHL inlet zone, which is subjected to low pressures and in liquid state. Therefore, it is usually not appropriate to use equation (1) to predict the shear strength of the fluid for both low and high fluid film pressures in the analysis of EHL when the fluid shear strength effect is incorporated. On the other hand, it is necessary and critically important to find the accurate prediction equation for the fluid shear strength at low pressures, i.e. in EHL inlet zones in the EHL analysis incorporating the fluid shear strength effect. It was pointed out by Zhang (2004a, 2001a) that the value of the shear strength of the fluid at low pressures may be insensitive to the variation of the pressure of the fluid and may usually be low. According to this, Zhang (2004a, 2001a, 2000) proposed the following equation for predicting the shear strength of the fluid for both low and high pressures, which may be applicable to the whole EHL contact: Equation 2 where p is the fluid pressure, p s is the fluid solidification pressure, τ l0 is the bulk fluid shear strength at ambient pressure, and α τl is the bulk fluid shear strength-pressure proportionality. The correctness and accuracy of equation (2) for predicting the shear strength of the usual fluid at both low and high pressures were confirmed by both the experimental results of Hoglund and Jacobson (1986) and the researches of EHL by Zhang et al. (2001a, 2002b, 2004a). Equation (2) usually predicts much lower shear strengths of the fluid at low pressures than equation (1). The analytical EHL results based on equation (2) as obtained by Zhang et al. (2001a, b, 2002b, 2004a) are qualitatively different from those based on equation (1) as obtained by Jacobson and Hamrock (1984) and Shieh and Hamrock (1991). Actually, the analytical EHL results based on equation (2) incorporating the fluid shear strength and contact-fluid interfacial slippage effects are very fresh and seem of a milestone in the research of EHL as can be found from the researches of EHL by Zhang et al. (2001b, 2002b, 2004a).
Zhang (2003a, 2004a, 2002a) proposed that precisely to say, in isothermal EHL, the material shear strength of effects is actually the contact-fluid interfacial shear strength instead of the fluid shear strength due to the maximum value of the fluid film shear stress across the film thickness occurring at the contact-fluid interface instead of within the fluid film in this EHL and thus the fluid film slippage occurring at the contact-fluid interface caused by the fluid film shear stress at the contact-fluid interface exceeding the contact-fluid interfacial shear strength. While, in EHL, the contact-fluid interfacial shear strength is the maximum endurable shear stress of the contact-fluid interface or the fluid shear strength, whichever is less. Zhang (2002a) further pointed out that in the analysis of EHL, when the contact-fluid interfacial shear strength is taken as the fluid shear strength, it actually gives an upper bound estimation on the contact-fluid interfacial shear strength effect in EHL. The EHL analysis incorporating the fluid shear strength effect referenced above all belong to this type of research. He suggested that it be necessary to take more accurate values of the contact-fluid interfacial shear strength to give more precise results of the contact-fluid interfacial shear strength effect in EHL by making more refined assumptions on the contact-fluid interfacial shear strength in the analysis of EHL.
Based on the assumption of the contact-fluid interfacial shear strength predicted by equation (2), Zhang (2004a, 2001b) established new rheological lubrication theories of EHL. In his theories, the mixed rheologies regime in EHL is proposed. His theories showed that in isothermal EHL of ideally smooth line contacts, viscoelastic continuum, viscoplastic continuum and non-continuum fluids are distributed from the inlet zone to the Hertzian contact zone in order for severe operating conditions when the contact-fluid interfacial shear strength is low in the inlet zone. In his theories, Zhang (2004a, 2001b) proposed to use the low values of the shear strength of the contact-fluid interface at low pressures, i.e. in EHL inlet zones for high bulk fluid temperatures varying from 0.5 to 20 MPa. He manifested that these low values of the shear strength of the contact-fluid interface at low pressures (in EHL inlet zones) are real by comparison to the experimental results obtained by others when the bulk fluid temperature is high. His theories showed that the molecularly thin fluid film occurs in the Hertzian contact zone in this mixed rheologies EHL and due to the non-continuum characteristics of this film across the film thickness, the rheological behavior of this film is qualitatively different from those of the viscoelastic continuum and viscoplastic continuum fluids, which respectively, simultaneously occur in different and other lubricated areas of this mixed rheologies EHL due to the relatively high fluid film thickness and thus the continuum characteristics of these fluids film across the film thickness in these lubricated areas. His theories revealed that in EHL, due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects, the overall EHL film can be severely thinning and lubricating films with different rheological behaviors can, respectively, simultaneously occur in different areas of the contact and thus be mixed in the whole contact. His theories may show a new mode of mixed EHL, where mixed rheologies occur in the contact. According to his theories, mixed EHL can occur even in the EHL of smooth concentrated contacts due to the occurrence of mixed rheologies in these EHL contacts. For an actual mixed EHL contact with contact surface roughness, the concept of mixed EHL may thus need to be revised, extended and generalized as the mixed EHL where lubricating films with different rheological behaviors can, respectively, simultaneously occur in different areas of the contact between the rough contact surfaces and may, respectively, locally occur in more irregular areas of the contact due to the local fluid film thinning and thickening in more irregular areas of the contact, respectively, due to the ridge penetration into and the furrow denting out of the fluid film of the contact surfaces, according to Zhang's (2004a, 2001b) theories. This more generalized mixed EHL concept well fits the experimental results of mixed EHL, respectively, obtained by Begelinger and Gee de (1974, 1976) and by Tabor (1981). It is of importance to the future modeling of mixed EHL and may help to define the configuration of the future mode of mixed EHL.
The present paper attempts to make a further and more clear justification on the contact-fluid interfacial shear strength in EHL due to its critical importance in this lubrication as described above, based on the recent researches carried out by the author on the fluid shear strength (Zhang, 2004c) and on EHL (Zhang, 2004a, b). This will help us to more clearly understand the scale of the value of the contact-fluid interfacial shear strength in EHL and its critical effects in this lubrication. The necessity of construction of new EHL theories based on the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects and the direction of the research of EHL in the following time will thus be clear.
2 Contact-fluid interfacial shear strength
Rozeanu and Snarsky (1978) proposed that there are three shear strengths in a hydrodynamic lubrication, i.e. the bulk fluid shear strength, the shear strength of the contact surface adhering layer and the shear strength of the contact surface adhering layer-bulk fluid interface. They theoretically showed that in a hydrodynamic lubrication, across the film thickness, the value of the shear strength of the contact surface adhering layer-bulk fluid interface is not greater than those of the bulk fluid shear strength and the shear strength of the contact surface adhering layer due to the occurrence of the entropy discontinuity at the contact surface adhering layer-bulk fluid interface. According to their research results, in a hydrodynamic lubrication, the maximum endurable shear stress of the contact-fluid interface is the shear strength of the contact surface adhering layer-bulk fluid interface. Its value is not greater than the value of the bulk fluid shear strength across the film thickness. In a hydrodynamic lubrication, across the film thickness, the contact-fluid interfacial shear strength thus seems to be the maximum endurable shear stress of the contact-fluid interface. However, for high bulk fluid temperatures, the value of the maximum endurable shear stress of the contact-fluid interface is very close to that of the bulk fluid shear strength across the film thickness in a hydrodynamic lubrication due to the melting of the contact surface adhering layer and then the weakening of the entropy discontinuity at the contact surface adhering layer-bulk fluid interface (Rozeanu and Snarsky, 1978). For this operating condition, the contact-fluid interfacial shear strength can be taken as the bulk fluid shear strength in the analysis of a hydrodynamic lubrication. Therefore, the study on the bulk fluid shear strength is still necessary and important for studying the contact-fluid interfacial shear strength effect in a hydrodynamic lubrication. This study is especially necessary and important for studying the contact-fluid interfacial shear strength effect in EHL, since high bulk fluid temperatures practically occurs in this lubrication especially in severe operating conditions. In the following sub-sections, results and comments are, respectively, presented on the maximum endurable shear stress of the contact-fluid interface in a hydrodynamic lubrication and the bulk fluid shear strength based on the recent researches by ourselves and the researches by others.
2.1 Maximum endurable shear stress of the contact-fluid interface
2.1.1 General theory
In a hydrodynamic lubrication, the value of the maximum endurable shear stress of the contact-fluid interface, i.e. the value of the shear strength of the contact surface adhering layer-bulk fluid interface is determined by the welding between the bulk fluid and the contact surface adhering layer. This welding is determined by the attraction forces between the bulk fluid molecules and the contact surface adhering layer molecules. It seems that this welding is determined by the temperature of the contact-fluid interface. For high bulk fluid temperatures or for high contact surface temperatures, the attraction forces between these molecules are usually greatly reduced due to the chemical and physical reactions and fluid thermal desorption at the contact surface adhering layer-bulk fluid interface. In this operating condition, the value of the shear strength of the contact surface adhering layer-bulk fluid interface usually can only be low (Czichos and Kirschke, 1972). In this operating condition, the bulk fluid pressure is not the factor that strongly influences the value of the shear strength of the contact surface adhering layer-bulk fluid interface. On the other hand, when the bulk fluid pressure is lower than the solidification pressure of the contact surface adhering layer-bulk fluid interface, the physical and chemical characters of the contact surface adhering layer-bulk fluid interface are not considerably changed by the bulk fluid pressure and the influence of the bulk fluid pressure on the value of the shear strength of the contact surface adhering layer-bulk fluid interface can be neglected. When the bulk fluid pressure is higher than the solidification pressure of the contact surface adhering layer-bulk fluid interface, the bulk fluid pressure considerably changes the physical and chemical characters of the contact surface adhering layer-bulk fluid interface and strongly influences the attraction forces and the shear strength between the bulk fluid molecules and the contact surface adhering layer molecules. Even for low contact surface temperatures, the above pressure influence on the shear strength of the contact surface adhering layer-bulk fluid interface may also be present.
Assume that: Equation 3 where p is the bulk fluid pressure, τ l is the shear strength of the contact surface adhering layer-bulk fluid interface, p s is the solidification pressure of this interface, α τl is constant, Δτ l and Δp are, respectively, the variations in τ l and p. Therefore, according to the fore paragraph and based on equation (3), the shear strength of the contact surface adhering layer-bulk fluid interface also satisfies equation (2).
According to the theoretical study on the variation of the fluid shear strength due to the pressurization and then the compression of the fluid by Zhang (2004c), equation (3) is correct when the fluid pressure is not extremely high (usually lower than 4 GPa). Therefore, according to the above theory and the theoretical study by Zhang (2004c), the maximum endurable shear stress of the contact-fluid interface, i.e. the shear strength of the contact surface adhering layer-bulk fluid interface in a hydrodynamic lubrication can usually be predicted by equation (2).
2.1.2 Factors that reduce the value of the maximum endurable shear stress of the contact-fluid interface
According to the theoretical and experimental results of Rozeanu and Snarsky (1978), in a hydrodynamic lubrication, the value of the maximum endurable shear stress of the contact-fluid interface is further reduced by the factors that make the transition of the entropy at the contact surface adhering layer-bulk fluid interface more ungradual (i.e. more discontinuous). These factors are typically, respectively:
- increasing the difference of the shear strength of the bulk fluid from that of the contact surface adhering layer and reducing the shear strength of the bulk fluid;
- making the contact surface adhering layer more unsolvable in the bulk fluid;
- highly ordering the molecules at the contact surface adhering layer-bulk fluid interface; and
- maintaining the equilibrium and highly ordered contact surface adhering layer.
Also, the following factors further significantly reduce the value of the maximum endurable shear stress of the contact-fluid interface in a hydrodynamic lubrication:
- physical or/and chemical thermal desorption at the contact surface adhering layer-bulk fluid interface at high contact surface temperatures; and
- inertia force effect of the fluid film in the condition of high rolling speeds.
The theoretical and experimental researches by Rozeanu and Tipei (1980) and Rozeanu and Snarsky (1977, 1978) showed that due to the above factors, in a hydrodynamic lubrication, the value of the shear strength of the contact surface adhering layer-bulk fluid interface, i.e. the value of the maximum endurable shear stress of the contact-fluid interface is practically rather limited. This very limited interfacial shear strength causes the fluid film slippage at the contact surface adhering layer-bulk fluid interface in the hydrodynamic lubrication even for modest rolling speeds. They experimentally showed that the contact-fluid interfacial slippage effect in a hydrodynamic lubrication due to this limited interfacial shear strength significantly reduces the load-carrying capacity of a hydrodynamic lubrication especially for high rolling speeds and heavy loads. They proposed that the hydrodynamic lubrication theory needs to be re-established due to the presence of the contact-fluid interfacial slippage in a practical hydrodynamic lubrication and thus the invalidation of the no-slip boundary condition postulated in conventional hydrodynamic lubrication theory.
2.2 Fluid shear strength
Zhang (2004c) studied by theory the shear strength of a fluid in the whole pressure range and especially in liquid state at low pressures for a given bulk fluid temperature. His study showed that when the fluid is in liquid state, i.e. at low pressures, the value of the shear strength of the fluid is insensitive to the variation of the pressure of the fluid and is low. When the fluid is in solidification state, i.e. at medium and high but not extremely high pressures, the value of the shear strength of the fluid is the most sensitive to the variation of the pressure of the fluid and is very approximately linearly increased with the increase of the pressure of the fluid. When the fluid is in high solidification state, i.e. at extremely high pressures, the value of the shear strength of the fluid is insensitive to the variation of the pressure of the fluid and is the highest, i.e. approaches to the value of the shear strength of the fluid in solid state. Figure 1 shows the dependence of the shear strength of a fluid on the fluid pressure in the whole pressure range for a given bulk fluid temperature, obtained by his study.
Zhang (2004c) showed that the value of the shear strength of a fluid in liquid state, i.e. at low pressures at ambient temperature is usually on the scale of 1 MPa. He showed that when the fluid is not subjected to extremely high pressures, i.e. not in high solidification state, the shear strength of the fluid can be predicted by equation (2) for a given bulk fluid temperature.
Zhang (2004c) showed by theory that for a given fluid, the influence of the bulk fluid temperature on the fluid shear strength versus fluid pressure curve as shown in Figure 1 is to translate this curve along the fluid pressure axis with an amount (i.e. the variation of the bulk fluid temperature does not change the value of the variation proportionality of the fluid shear strength with the fluid pressure when the fluid is in solidification state). Figure 2 shows the influence of the bulk fluid temperature on the fluid shear strength versus fluid pressure curve for a given fluid theoretically derived by Zhang (2004c). According to Figure 2, when the bulk fluid temperature is high enough, the value of the shear strength of the fluid is low even for the pressure of the fluid on the scale of 1 GPa. This result is well confirmed by Hoglund and Jacobson's (1986) experiments. According to their experiments, the translation effect of the bulk fluid temperature on the fluid shear strength versus fluid pressure curve described above is very significant when the bulk fluid temperature is over ambient temperature. Therefore, in the certain range of the bulk fluid temperature, the increase of the bulk fluid temperature significantly reduces the shear strength of the fluid for a given pressure and for high bulk fluid temperatures the shear strength of the fluid usually can only be low. These results for the fluid shear strength are same with the results of the maximum endurable shear stress of the contact-fluid interface in a hydrodynamic lubrication for high bulk fluid temperatures as described in Section 2.1.1.
The theory of the fluid shear strength derived by Zhang (2004c) as shown by Figures 1 and 2 is well supported by experiments.
2.3 Comments
2.3.1 Prediction equation for the contact-fluid interfacial shear strength in EHL
In the experiment of fluid rheology, one may be difficult to distinguish whether his observed fluid rheological behavior is due to the fluid shear strength effect or due to the effect of the maximum endurable shear stress of the contact-fluid interface. Therefore, he may be difficult to distinguish whether the limiting shear stress of his observed fluid (shear stress versus shear strain rate) rheological curve is the fluid shear strength or the maximum endurable shear stress of the contact-fluid interface. In experiments, these two parameters are important to the fluid rheological behavior but are really difficult to distinguish from one another. However, in the analysis of EHL in isothermal condition, this does not matter. In this analysis, the parameter of the contact-fluid interfacial shear strength is only necessary to be used while the parameters of the fluid shear strength and the maximum endurable shear stress of the contact-fluid interface both are not appearing. Also, in this analysis, the contact-fluid interfacial shear strength does not need to be critically distinguished as the fluid shear strength or the maximum endurable shear stress of the contact-fluid interface but is the minimum of them. Since the fluid shear strength and the maximum endurable shear stress of the contact-fluid interface in a hydrodynamic lubrication both are predicted by equation (2) as shown above, the contact-fluid interfacial shear strength in this analysis is also predicted by equation (2). In this prediction equation for the contact-fluid interfacial shear strength, the parameter p s is not critically distinguished as the bulk fluid solidification pressure or the solidification pressure of the contact-fluid interface and is one of them.
2.3.2 Support and verification to the present theory of the contact-fluid interfacial shear strength
Besides by the present theory as shown above, the prediction equation for the contact-fluid interfacial shear strength in EHL expressed by equation (2) has also been supported and verified by a lot of other researches. Zhang et al. (2001a, 2002b, 2004a) developed the EHL theory based on the assumption of the contact-fluid interfacial shear strength predicted by equation (2). His theory well matches the experimental EHL film thickness obtained by Kannel and Bell (1971) and validates this prediction equation for the contact-fluid interfacial shear strength in EHL. The experiment by Hoglund and Jacobson (1986) also verifies this prediction equation for the contact-fluid interfacial shear strength in EHL.
3 Contact-fluid interfacial slippage
In a hydrodynamic lubrication, the contact-fluid interfacial slippage is one of the effects of the contact-fluid interfacial shear strength, caused by the fluid film shear stress at the contact-fluid interface exceeding the contact-fluid interfacial shear strength. Rozeanu and Tipei (1980) and Rozeanu and Snarsky (1977, 1978) verified by experiments that the contact-fluid interfacial slippage practically occurs in a hydrodynamic lubrication. This also occurs in EHL. Zhang et al. (2002a, 2003b) provided the theoretical analysis and physical background of the contact-fluid interfacial slippage in isothermal EHL of line contacts. In experiments, Kaneta et al. (1990) observed the loss of the fluid film adherence to the contact-fluid interface and the fluid film slippage at the contact-fluid interface, i.e. the contact-fluid interfacial slippage in EHL. Kaneta et al. (1996) experimentally observed dimples of sliding EHL point contacts at medium loads; Zhang et al. (2002b) suggested that these dimples be caused by the combined effect of the contact-fluid interfacial slippage and fluid film viscous heating in EHL.
4 Contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects in EHL
4.1 Mechanisms
4.1.1 Mechanisms in isothermal EHL of ideally smooth concentrated contacts
Rozeanu and Tipei (1980) and Rozeanu and Snarsky (1977, 1978) experimentally showed that in a sliding hydrodynamic bearing, the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects reduce the fluid film pressure and the load-carrying capacity. They studied by experiment the influence of various factors such as bulk fluid temperature, tiny solid particles and chemical additives in fluids and inertia effects on the contact-fluid interfacial shear strength and contact-fluid interfacial slippage and then on their effects in a sliding hydrodynamic bearing. They proposed that in a sliding hydrodynamic bearing, the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects cause the difference of the velocity of the fluid film at the contact surface from the speed of that contact surface, then cause the change of the velocity distribution of the fluid film across the film thickness and thus the reduction of the pressure within the fluid film. They showed by experiments that the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects cause the load-carrying capacity of a hydrodynamic bearing much lower than conventional hydrodynamic lubrication theory prediction.
In experiments, the observation of the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects in EHL is much more difficult than in a plain hydrodynamic bearing due to the small contact width, extremely thin fluid film and very short transit time of an EHL contact. Zhang et al. (2001a, 2002a, b, 2000) observed by numerical simulation the similar phenomena in isothermal EHL of ideally smooth line contacts due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects as Rozeanu et al. (1977, 1978, 1980) observed in a sliding hydrodynamic bearing. Zhang et al. (2002a) analytically showed that in EHL, the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects cause the difference of the velocity of the fluid film at the contact surface from the speed of that contact surface and the changes of the pressure distribution and especially the pressure gradients within the fluid film. As a result of these effects, in the condition of large slide-roll ratios (e.g. slide-roll ratios over 1), the Couette flow through the EHL contact is significantly reduced and the Poiseuille flow through the EHL contact is significantly increased, respectively, due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects on the fluid film velocity at the contact surfaces and the pressure gradients within the fluid film. These then cause the significant reduction of the total fluid mass flow through the EHL contact. This causes the significant reductions of the global EHL film thickness and the EHL load-carrying capacity. Zhang et al. (2002a) analytically showed that the mechanism of the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects on the EHL load-carrying capacity is the change of the total fluid mass flow through the EHL contact caused by these effects. He showed that the great reduction of the EHL load-carrying capacity due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects is essentially caused by the great reduction of the total fluid mass flow through the EHL contact due to these effects. Zhang et al. (2002a) also showed by numerical simulation that in EHL, the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects cause the reduction of the local fluid film pressure and thus the reduction of the local fluid film thickness due to the local elastic rebounding of the contact surfaces caused by this local fluid film pressure reduction.
4.1.2 Mechanisms in isothermal EHL of rough concentrated contacts, i.e. in mixed EHL of isothermal condition
In isothermal EHL of rough line contacts, i.e. in mixed EHL of isothermal line contacts, besides the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects in isothermal EHL of ideally smooth line contacts shown in the above section, Zhang (2003b) showed by numerical simulation for simple sliding that the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects generate the ripples of the fluid film velocities at the contact surfaces in combination with the contact surface roughness effect, remove the ripples of the fluid film pressure, and make the initial contact surface roughness persist. These generated phenomena are absent in a mixed EHL when the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects are neglected. The mechanism of these phenomena is the fluid film slippage at the contact surfaces of this mixed EHL contact. Therefore, the contact-surface interfacial shear strength and contact-fluid interfacial slippage effects are very important in a mixed EHL and need to be incorporated in the theoretical modeling of a mixed EHL especially in severe operating conditions. Conventional mixed EHL theory failed to do this. New mixed EHL theory is therefore necessary to be established by incorporating the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects in a mixed EHL.
4.2 Mixed rheologies in isothermal EHL of ideally smooth concentrated contacts due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects
Zhang et al. (2002b, 2004a) analytically showed that in isothermal EHL of ideally smooth line contacts, due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects, the EHL film thickness especially in the Hertzian contact zone is usually extremely low and on the nanometer scale even in pure rolling for severe operating conditions, i.e. the condition of heavy loads, high rolling speeds and high bulk fluid temperatures. This especially occurs for large slide-roll ratios in severe operating conditions. Zhang et al. (2002b, 2004a) analytically showed that in this case, due to the simultaneous occurrences of the contact-fluid interfacial slippage in part of the EHL contact and the molecularly thin EHL film in the Hertzian contact zone, viscoelastic continuum, viscoplastic continuum and non-continuum fluids simultaneously occur from the inlet zone to the Hertzian contact zone in order. Zhang et al. (2002b, 2004a) showed that the rheological behaviors of these fluids are different from each other. Therefore, mixed rheologies occur in the EHL contact for this case. This may represent a new mode of mixed EHL. This new mode of mixed EHL shows that mixed lubrication can occur even in EHL of ideally smooth concentrated contacts due to the occurrence of mixed rheologies in this EHL contact. The conventional concept of mixed EHL may therefore need to be revised. The new and advanced mode of mixed EHL may therefore need to be generalized as the mode of mixed EHL in which mixed rheologies can occur. This new mode of mixed EHL may be important in the future. It may be a direction of the researches of EHL and mixed EHL in the future.
Figure 3 typically shows the lubrication regime chart in isothermal EHL of ideally smooth line contacts for a slide-roll ratio due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects. In Figure 3, when the EHL is in the viscoelastic-fluid regime zone, the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects are absent, the EHL film is relatively thick in the whole EHL contact, and the EHL fluid is viscoelastic in the entire area of the EHL contact. When the EHL is in the viscoplastic-fluid regime zone, the EHL film is relatively thick in the whole EHL contact, however, viscoelastic and viscoplastic continuum fluids, respectively, simultaneously occur in different parts of the EHL contact, the viscoelastic continuum fluid mainly occurs in the EHL inlet zone, and the viscoplastic continuum fluid mainly occurs in the Hertzian contact zone due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects. When the EHL is in the non continuum-fluid regime zone, viscoelastic continuum, viscoplastic continuum and non continuum fluids, respectively, simultaneously occur in different parts of the EHL contact, the viscoelastic continuum fluid mainly occurs in the EHL inlet zone, the viscoplastic continuum fluid mainly occurs from the inlet zone to the Hertzian contact zone due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects and the relatively thick EHL film in this area, and the non continuum fluid mainly occurs in the Hertzian contact zone due to the molecularly thin EHL film presence in this zone caused by the EHL film extreme thinning and the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects. Figure 3 shows that in EHL, due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects, the viscoelastic-fluid regime usually occurs in the operational scopes of low loads and low rolling speeds, the viscoplastic-fluid regime usually occurs in the operational scopes of low and medium loads and low and medium rolling speeds, and the non continuum-fluid regime usually occurs in the operational scopes of relatively heavy loads. While, mixed rheologies occurs in both the viscoplastic-fluid and non continuum-fluid regime zones. These show that mixed rheologies as well as molecularly thin EHL film occur in EHL in a fairly wide operational scope, due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects. The above proposed new and advanced mode of mixed EHL incorporating mixed rheologies in EHL is therefore obviously of significant practical interest.
4.3 New mode of mixed EHL due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects
Zhang (2004b) showed by numerical simulation results that dry contact can indeed locally occur in the EHL contact when the EHL contact is in the non continuum-fluid regime zone described above, i.e. in molecularly thin fluid film lubrication, due to the surface pressure effect, i.e. the Van der Waals and solvation pressure effects between the contact surfaces which locally cause very large attractive pressures between the two contact surfaces and thus make the two contact surfaces locally in adhesion with one another in the EHL contact. He proposed that the dry contact regime between the contact surfaces needs to be incorporated into a practical mode of mixed EHL when theoretically modeling a mixed EHL. According to the above proposed new mode of mixed EHL and the research results of EHL obtained by Zhang (2004b), when the contact surface roughness is further incorporated into a practical mode of mixed EHL, due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects, a more practical mode of mixed EHL for the theoretical modeling of mixed EHL may need to be further generalized as the mode of mixed EHL where lubricating films with different rheological behaviors and dry contact can, respectively, simultaneously occur in different areas of the contact between the rough contact surfaces and may, respectively, locally occur in more irregular areas of the contact due to the local fluid film thinning and thickening in more irregular areas of the contact, respectively, due to the ridge penetration into and the furrow denting out of the fluid film of the contact surfaces. The typical feature of this new generalized mode of mixed EHL is mixed contact regimes between the contact surfaces in a mixed EHL contact. These mixed contact regimes include fluid films with different rheological behaviors between the contact surfaces, respectively, simultaneously occurring in different and maybe irregular lubricated areas of a mixed EHL contact and thus mixed in a whole mixed EHL contact and the local dry contact between the contact surfaces. The defined dry contact in EHL in the previous paper of Zhang (2004b) includes the metal to metal contact and the contact between the oxidized chemical boundary layers of the two contact surfaces, i.e. the oxidized chemical boundary layers contact. In the present defined new and generalized mode of mixed EHL, the dry contact between the contact surfaces may need to particularly refer to the metal to metal contact. While, the regime of the contact between the local oxidized chemical boundary layers of the two contact surfaces, i.e. the regime of local chemical boundary layer lubrication between the contact surfaces may need to be added into the present new and generalized mode of mixed EHL and taken as a kind of contact regime between the contact surfaces. According to these statements, the present defined new mode of mixed EHL is therefore further generalized by incorporating the regime of the contact between the local oxidized chemical boundary layers of the contact surfaces into this mode of mixed EHL. According to these results, the new and generalized mode of mixed EHL proposed in the present paper is shown in Figure 4.
The present new and generalized mode of mixed EHL shown in Figure 4 is well confirmed by the experimental results of mixed EHL, respectively, obtained by Begelinger and Gee de (1974, 1976) and by Tabor (1981) as reviewed in the paper of Zhang (2004b). It is obviously of substantial and much more progress in the understanding of a real mixed EHL than conventional modes of mixed EHL as proposed in the theoretical modeling of mixed EHL previously. It may be important for the theoretical modeling of mixed EHL in the future. It may be a direction of the theoretical research of mixed EHL in the future.
5 Conclusions
This paper reviews the contact-fluid interfacial shear strength and its critical importance in EHL, based on the previous researches on this topic by others and by the present author. It is proposed that in a hydrodynamic lubrication including EHL, the contact-fluid interfacial shear strength is the maximum endurable shear stress of the contact-fluid interface or the fluid shear strength, whichever is less. The maximum endurable shear stress of the contact-fluid interface and the fluid shear strength both are usually universally predicted by the following equation for isothermal condition: Equation 4 where p is the fluid pressure, p s is the bulk fluid or contact-fluid interface solidification pressures, τ l0 is the bulk fluid shear strength or the maximum endurable shear stress of the contact-fluid interface at ambient pressure, and α τl is the bulk fluid shear strength or the maximum endurable shear stress of the contact-fluid interface-pressure proportionality. Therefore, in the analysis of an isothermal hydrodynamic lubrication including isothermal EHL, the contact-fluid interfacial shear strength does not need to be critically distinguished as the fluid shear strength or the maximum endurable shear stress of the contact-fluid interface and is also predicted by equation (2). In this prediction equation for the contact-fluid interfacial shear strength, the parameter τ l is not critically distinguished as those of the bulk fluid or the contact-fluid interface and is the parameter of one of them, and the parameters p s, τ l0 and α τl are, respectively, correspondingly distinguished. In the analysis of EHL in isothermal condition, the parameter of the contact-fluid interfacial shear strength is only necessary to be used while the parameters of the fluid shear strength and the maximum endurable shear stress of the contact-fluid interface both are absent. In this analysis, the contact-fluid interfacial shear strength is simply predicted by equation (2). Equation (2) shows that in a hydrodynamic lubrication including EHL, when the fluid film pressure is low, the value of the contact-fluid interfacial shear strength is insensitive to the variation of the fluid film pressure and is usually low since the value of the contact-fluid interfacial shear strength τ l0 at ambient pressure is usually low. When the fluid film pressure is medium and high (but not extremely high), the value of the contact-fluid interfacial shear strength is linearly increased with the increase of the fluid film pressure.
The mechanisms of the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects in EHL and mixed EHL are reviewed, analyzed and presented for a correct understanding on these effects in EHL.
It is pointed out that the contact-fluid interfacial shear strength effect is practically very important in EHL. It practically causes the contact-fluid interfacial slippage in EHL. As a result, the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects significantly reduce the load-carrying capacity of EHL especially in severe operating conditions, i.e. for heavy loads, high rolling speeds, large slide-roll ratios and high bulk fluid temperatures. This has been well proved by both the experiments of Rozeanu (1977, 1978, 1980) on hydrodynamic lubrication in sliding bearings and the researches of Zhang et al. (2001a, b, 2002a, b, 2003a, b, 2004a, 2000) on EHL.
Owing to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects and the extreme EHL film thinning especially in the Hertzian contact zone caused by these effects, in isothermal EHL of ideally smooth concentrated contacts in severe operating conditions, mixed rheologies usually occur in the EHL contact, i.e. viscoelastic continuum, viscoplastic continuum and non-continuum fluids usually simultaneously occur from the inlet zone to the Hertzian contact zone in order. The rheological behaviors of these fluids are different from each other. This may represent a new mode of mixed EHL. This new mode of mixed EHL shows that mixed lubrication can occur even in EHL of ideally smooth concentrated contacts due to the occurrence of mixed rheologies in this EHL contact. The conventional mode of mixed EHL may therefore need to be revised, extended and more generalized as the new and advanced mode of mixed EHL in which mixed rheologies can occur.
According to this new mode of mixed EHL and the research results on dry contact in EHL obtained by Zhang (2004b), when the contact surface roughness and the regime of the contact between the local oxidized chemical boundary layers of the contact surfaces both are further incorporated into a practical mode of mixed EHL, due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects, a more practical mode of mixed EHL for the theoretical modeling of mixed EHL may need to be further revised, extended and generalized as the mode of mixed EHL where fluid films with different rheological behaviors, oxidized chemical boundary layer lubrication and dry contact can, respectively, simultaneously occur in different areas of the contact between the rough contact surfaces and may, respectively, locally occur in more irregular areas of the contact due to the local fluid film thinning and thickening in more irregular areas of the contact, respectively, due to the ridge penetration into and the furrow denting out of the fluid film of the contact surfaces. The typical feature of this most generalized mode of mixed EHL is mixed contact regimes between the contact surfaces in a mixed EHL contact. These mixed contact regimes include fluid films with different rheological behaviors between the contact surfaces, respectively, simultaneously occurring in different and maybe irregular lubricated areas of a mixed EHL contact and thus mixed in a whole mixed EHL contact, the local oxidized chemical boundary layer lubrication between the contact surfaces and the local dry contact between the contact surfaces. In this most generalized mode of mixed EHL, the dry contact between the contact surfaces refers to the metal to metal contact.
This most generalized mode of mixed EHL is well supported by the experimental results of mixed EHL, respectively, obtained by Begelinger and Gee de (1974, 1976) and by Tabor (1981). It is obviously of substantial and much more progress in the understanding of a real mixed EHL than conventional modes of mixed EHL as proposed in the theoretical modeling of mixed EHL previously. It may be important for the theoretical modeling of mixed EHL in the future. It may be a direction of the theoretical research of mixed EHL in the future.
Equation 1
Equation 2
Equation 3
Equation 4
Figure 1Typical illustration of the shear strength of a fluid versus fluid pressure curve in the whole range of pressure for a given bulk fluid temperature
Figure 2Typical illustration of the shear strength of a fluid versus fluid pressure curves in the whole range of pressure for different bulk fluid temperatures
Figure 3Typical illustration of the lubrication regime chart in isothermal EHL of ideally smooth line contacts for a slide-roll ratio due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects. G=4,500, R=6 mm, C
0=4.78E-6, S=1.0
Figure 4Generalized mode of mixed EHL proposed in the present paper
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Further Reading
Cioc, C., Cioc, S., Moraru, L., Kahraman, A., Keith, T.G. (2002), "A deterministic elastohydrodynamic lubrication model of high-speed rotorcraft transmission components", Trib. Trans., Vol. 45 pp.556-62.
Zhang, Y. (2005), "How does dry contact occur in elastohydrodynamic lubrication?", Ind. Lubri. & Trib., Vol. 57 No.5, .
Zhang, Y. (2006), "Shear strength of a fluid in the whole ranges of pressure and temperature", Ind. Lub & Trib., Vol. 58 No.2, .
Zhang, Y., Wen, S. (2000), "EHL performance of the lubricant with shear strength: Part I-Boundary slippage and film failure", Trib. Trans., Vol. 43 pp.700-10.
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