Low Reynolds number friction reduction with polymers and textures
Introduction
We have previously shown that surface textures reduce friction with viscous Newtonian oils in lubricated sliding contact [1], [2], [3]. At high sliding speeds (shear rates), high viscosity oils can exhibit viscous heating effects, which decrease their apparent viscosity and cause a drop in normal force; one method to reduce viscous heating effects is to add polymers to Newtonian oils to obtain better viscosity-temperature and viscosity-pressure dependence [4], [5], [6], and to increase the load carrying capacity (normal force) [7]. This change in rheology due to the addition of polymers has been studied numerically using a generalized Newtonian fluid (GNF, which gives purely viscous shear thinning effects) as the lubricant in journal bearings, thrust bearings, and elasto-hydrodynamic (EHL) contact. These studies show that the eccentricity of the journal and the load carrying capacity correlate to the lubricant rheology [4], [8], [9], [10], [11], [12], [13], [14] where lower viscosity fluids give smaller normal forces. Experiments have also been performed with the assumptions that the lubricant can be modeled as a GNF, and again show shear thinning leads to smaller normal forces [15].
The above models, however, do not take into account the viscoelasticity that occurs in Non-Newtonian lubricants; GNF models only take into account purely viscous shear thinning/thickening effects. Viscoelasticity, even under steady shear, can lead to first and second normal stress differences (N1 and N2 respectively) [16], which can increase the load carrying capacity of the bearing. For thin film flow, Tichy [17] derived a modified Reynolds equation in Cartesian coordinates that can be used for textured surfaces using the upper-convected Maxwell model, which takes into account the viscoelasticity of the lubricant and allows for the generation of first normal stress differences. He showed that for a converging flow field, viscoelastic effects increase the pressure, resulting in a larger load carrying capacity. Zhang and Li [18] and Li [19] performed perturbation analyses for the flow field, shear stresses, and pressure using the upper-convected Maxwell model and the Phan-Thien–Tanner (PTT) model respectively, and showed that viscoelasticity can significantly enhance the pressure in thin film flows. Harnoy [20] also derived a modified Reynolds equation for journal bearings using the Oldroyd B model (i.e. upper-convected Maxwell plus Newtonian solvent), and showed that viscoelasticity can increase the load carrying capacity and decrease vibration effects. Williamson et al. [21] measured the effects of viscoelastic lubricants in a journal bearing simulator, and showed that viscoelastic effects have a beneficial effect on lubrication characteristics.
While the upper-convected Maxwell model and Oldroyd-B model include viscoelastic normal stress differences in the modified Reynolds equations, they do not include shear thinning effects. The use of higher fidelity models (such as the PTT, Giesekus [22], etc.) in the modified Reynolds equation corrects for this modeling inaccuracy, since higher fidelity models can include shear thinning and normal stress differences. However, the commonly-used Reynolds equations do not include inertial effects, which will be important for low viscosity oils and have been shown to increase normal forces [4], [23].
Work has also examined surface textures on friction reduction with Non-Newtonian lubricants. Broboana, Tanase, and Balan [24] performed numerical simulations for a textured thrust bearing with a GNF model. They observed a lower shear stress on the moving plate with the combined texture and Non-Newtonian fluid configuration when compared to only having textures. Rajagopal and Das [25] showed through numerical simulations that 2-D symmetric textures decrease drag, and the drag reduction is dependent on the Wi. Kango et al. [26] performed numerical analysis on a textured journal bearing (with spherical and elliptical bottom profile textures, i.e. symmetric textures) using a power law GNF model with cavitation effects, and observed an increse in load carrying capacity for shear thickening fluids when the texture depth was less than 30 µm. Khatri and Sharma [27], Kango and Sharma [28], and Li et al. [29] also performed numerical analysis for textured journal bearings with a power law GNF, and showed that using textures and shear thinning reduces the frictional torque from the flat and Newtonian case, but shear thinning reduces the load carrying capacity. Sharma and Yadav [14] performed numerical analysis for a textured thrust bearing (with circular and conical bottom texture profiles which are again symmetric) with a power law GNF model, and showed again that shear thickening fluids increase the load carrying capacity of the bearing. These results, however, focused on symmetric textures, and neglected the lubricant’s viscoelasticity, which could enhance the results.
The work presented here is an experimental investigation on the effects of surface texture depth profiles on friction reduction with a viscoelastic lubricant (polymer solution) and texture asymmetry. Gap controlled experiments were performed on a custom tribo-rheometer to systematically examine the friction reduction with varying Reynolds number (Re here Reh ∈ [0.11, 16.1]), Weissenberg number (Wi= where is the nominal shear rate, here Wi ∈ [0.088, 33.3]) and Deborah number (De=λ/ttrans, here De ∈ [0.0045, 0.45]). The moving top plate was allowed to rotate in both directions to determine direction of motion dependence on the normal force production and shear stress reduction. Cavitation effects are not observed; therefore the normal force produced is solely due to the fluid-texture interaction and the lubricant’s viscoelastic properties.
Section snippets
Materials and methods
Fig. 1 shows a schematic of our experimental setup, the same previously used to test surface textures and Newtonian fluids [1], [2]. The custom setup consists of a gap-controlled rotational rheometer (combined motor-transducer, DHR-3, TA Instruments) that could accurately measure the torque and normal force produced by shearing a polymer solution between two parallel surfaces. The normal force is measured using a force rebalancing transducer coupled to the top (moving) plate with a manufacturer
Pipkin space
We can represent the response of the polymer solution flowing over the surface textures through the use of a dimensional and non-dimensional Pipkin space, which gives regions where flow strength and transient effects are important [52], [53]. In the dimensional Pipkin space, the time scales of importance are determined solely by the plate velocity and geometry of the surface texture. We define our transient timescale of the flow similar to previous work in the literature [34], [35], [39], [54]
Results and discussion
We collected data with the 0.54wt% PIB at the three gap heights given in Fig. 3; however, for results with textures we focus attention on data at the smallest gap height, h=269 µm. The smallest gap produces the largest torques and normal forces due to the associated higher shear rates. We note that the trends observed are the same at all the gap heights tested.
Conclusions
We have systematically tested the effects of surface texture depth profiles on friction reduction with a polymer solution for varying Reh, Wi, and De. We showed that the shear stress on the flat plate can be lowered through shear thinning, resulting in a lower apparent viscosity. Surface textures are able to reduce the shear stress beyond that seen by shear thinning, until secondary flow effects become important.
The flat plate produces measurable normal forces above the experimental limit due
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors wish to thank the members of the MechSE machine shop who created the surface textures used in the experiments. This work was supported by the Engineering Research Center for Compact and Efficient Fluid Power (CCEFP) with support from the National Science Foundation under grant no. EEC-0540834, and by the National Science Foundation under grant no. CMMI-1463203.
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