Elsevier

Tribology International

Volume 131, March 2019, Pages 386-397
Tribology International

Crucial role of solid body temperature on elastohydrodynamic film thickness and traction

https://doi.org/10.1016/j.triboint.2018.11.006Get rights and content

Highlights

  • Solid body temperature effect (TsolidToil) exists in traction tests with disc machines.

  • A quantitative thermal EHL model was built to analyze this effect.

  • Solid body temperature affects the EHL film temperature and film thickness significantly.

  • Simple film thickness prediction method with body temperature effect is given.

  • For extremely high speeds, inlet shear and compressive heating were discussed.

Abstract

The effect of the solid body temperature effect on film thickness and traction in elastohydrodynamic lubrication (EHL) has been studied numerically. At a moderate entrainment velocity, the EHL film behavior is controlled by the solid body temperature as the oil heats up to the body temperature before entering the contact zone and thus the film thickness decreases. For high velocity conditions, inlet shear and compressive heating also contribute to the reduction of film thickness. The results indicate that the measured film thickness and traction on disc machines might be lower than the expected values when the disc temperature exceeds the supplied oil temperature.

Introduction

Traditional thermal EHL simulations are mainly based on the assumption that solid body temperature equals the supplied oil temperature. However, for the experimental validation of the EHL theory, e.g. during traction measurements using a twin-disc machine, it may take long for the test rig to reach thermal equilibrium and the disc body temperature rarely remains constant with varying slide-to-roll ratios (SRRs). Hence, the fluid behavior and the corresponding measured friction and film thickness might be influenced by the solid body temperature. This effect is investigated in this work.

It has been known that thermal effects are important in EHL since the 1960s [1,2]. For point contacts, the first full numerical solution was obtained by Zhu and Wen [3], who solved the three-dimensional energy equations of the oil and the solids. Kim and Sadeghi [4,5] carried out thermal EHL simulations at high loads, using the multigrid methods introduced into EHL by Lubrecht [6] and Venner [7]. Their results illustrated significant temperature rises in the film. They did not solve the solid energy equation to get the temperature distribution in the contacting solids. Yang and co-workers [8,9] developed a thermal EHL model, which includes the three-dimensional temperature fields of the film and the solids. Their results showed that at high SRRs thermal effects are important for all aspects of EHL behavior, such as film shapes, pressure and temperature distributions.

In the aforementioned models the lubricant was assumed to behave Newtonian. However, even the simple organic liquid behaves in a highly non-Newtonian way [10,11] in the high pressure contact region, especially when there is sliding. Therefore, the ability to predict EHL traction using a standard thermal Newtonian model is limited. It has also been shown that, for high-molecular-weight base oil and polymer-blended oil even under pure rolling conditions, inlet shear thinning occurs [11,12], which also cannot be captured by a Newtonian fluid model. Since the numerical simulation in 1984 by Zhu [13], several non-Newtonian fluid models have been used in thermal EHL analysis of point contacts, such as using the Eyring model [[13], [14], [15], [16]], the Carreau-type models [[17], [18], [19]], or some hybrid models [20]. All results show that non-Newtonian effects have a great influence on EHL traction. Recently, based on viscometer measurements and molecular dynamics, Bair et al. [21] pointed out that shear-thinning in EHL follows a power-law (e.g. Carreau model) rather than the logarithmic response of the Eyring model that is usually assumed in EHL simulations [[13], [14], [15], [16]]. Using a modified Carreau-Yasuda model [22] for the shear-thinning, Habchi et al. [17] presented a full-system finite element method for the thermal non-Newtonian problem. They measured the transport properties of the Shell-T9 mineral oil and then derived rheological parameters [18] to describe the dependencies. The derived models were used in the thermal EHL solver. Their numerical results of the film thickness showed good agreements with the experiments, while the simulated friction coefficient agreed partly with their experiments mainly at high SRRs for the considered operating conditions [18]. This kind of quantitative approach [23], in which the measured viscosity and density properties are used in the simulation to predict the EHL behavior, has contributed a lot in the understanding of EHL film thickness and traction [18,24]. Over a combination of larger velocity and pressure ranges, also based on a Carreau-type model, Björling et al. [19] quantitatively compared the deviations of the friction coefficient between numerical calculations and experiments using squalane as the lubricant. The deviation at high speeds can be larger than 10%. They gave one possible explanation that during the ball-on-disc traction measurements the surface temperature of the ball was gradually increasing, but in their model the solid body temperature was not considered.

In practice, the solid body temperature can exceed the supplied oil temperature. Isaac et al. [25] showed that there are differences of the friction coefficient measured with different traction machines under similar operating conditions. They studied the heat flow of the twin-disc machine using a thermal network method and revealed that the disc bulk temperature has a significant impact on the measured friction coefficient [25]. During their traction tests, the discs heat up and it was recorded that the disc bulk temperature can be 45°C higher than the supplied oil temperature. Effects of body temperature on traction measurements were also reported recently by Bader et al. [26], and see also Appendix 1, which shows the evolution of the disc mass temperature and traction coefficient during repeated traction curve experiments. The shape of the traction curves is affected by the increasing disc mass temperature. The effect of the solid body temperature also exists in many other test rigs and may affect the test results, e.g. in scuffing tests with a FZG test rig [27] and in smearing tests with a ring-roller-ring test rig [28]. So far in single EHL contact simulations, solid body temperature effects have not received much attention. Liu and Yang [29,30] analyzed the solid body temperature effect on EHL behavior using Newtonian and Eyring-type fluid models. They found that the solid body temperature is more important than the supplied oil temperature at low entraining velocities for the film thickness, whereas at high velocities there is only weak effect of the solid body temperature [29].

In this study, the effect of solid body temperature on EHL film thickness and traction is investigated in a thermal steady state point contact problem using the Carreau-Yasuda shear thinning model. The rheological models for Shell T9 mineral oil in Ref. [18] are adopted to describe the pressure and temperature dependence of the transport properties (e.g. viscosity, density, thermal conductivity). Under high velocity conditions, inlet shear heating and compressive heating cannot be ignored, which may work together with the solid body temperature effect to affect the inlet film temperature and thus the film thickness. Another aim of the study is to reveal the important role of solid body temperature effect in the traction curve experiments with disc machines, as this is not addressed in the former work [29,30].

Section snippets

Theoretical models

The contact region of an EHL rolling/sliding circular contact is illustrated in Fig. 1 [29]. The two bodies, soild-1 and solid-2, are loaded together and deform elastically to form a circular contact with Hertzian radius a. The surface velocities are u1 and u2, respectively, and a thin film is formed in the approximately parallel conjunction to carry the load. At the left edge (where x=xin), the boundary temperatures of soild-1 and solid-2 are Ts1 and Ts2, respectively, whereas the inlet

Numerical solution

The equations and the boundary conditions were solved in dimensionless form. The non-dimension parameters are given in the Nomenclature and they are mainly referred to the Hertzian contact parameters, the entraining speed, and the fluid properties at ambient conditions. Subsequently, they were discretized using finite difference method (FDM).

The numerical solution is achieved by an iterative process consisting of pressure-film computation cycles (PH cycles) and temperature-shear rate cycles (T¯Γ

Results and discussion

Steel-steel circular contacts lubricated with Shell T9 are considered for pure-rolling and rolling/sliding conditions. The temperature of the supplied oil T0 is 333K(60°C). Three solid body temperatures are employed and they are addressed by Ts¯ (see Eq. (12)), where Ts¯=1.00 means the solid body temperature is equal to the supplied oil temperature as Ts=T0=333K(60°C), Ts¯=1.05 means Ts=1.05T0=350K(77°C), and Ts¯=1.10 means Ts=1.10T0=366K(93°C). Table 2 shows the input parameters and material

Conclusions

The effect of solid body temperature on EHL traction, film thickness and film temperature rise has been investigated by numerical simulation with a non-Newtonian thermal EHL model for circular contact. Physically sound rheological models of the lubricant, such as Carreau-Yasuda shear thinning and free volume density models, were adopted and incorporated into the EHL solver to describe the fluid behavior. The traction reduction phenomenon (Appendix 1) in the disc-machine experiments is explained

Acknowledgements

The authors would like to thank Prof. CH Venner for helpful discussion and for careful correction of the manuscript, and Mr. T Brieke and Mr. T Terwey on the re-design of the disc machine. This work is partly supported by FVV, Research Association for Combustion Engines e.V., Germany, through Grant No. 6012773. The first two authors, Liu and Zhang, thank the China Scholarship Council for providing the PhD scholarship.

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