Research Papers: Design of Energy, Fluid, and Power Handing Systems

Enhancing Full-Film Lubrication Performance Via Arbitrary Surface Texture Design

[+] Author and Article Information
Yong Hoon Lee

Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: ylee196@illinois.edu

Jonathon K. Schuh

Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: schuh4@illinois.edu

Randy H. Ewoldt

Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: ewoldt@illinois.edu

James T. Allison

Industrial and Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: jtalliso@illinois.edu

1Corresponding author.

This work was presented in part at the 42nd ASME Design Automation Conference, Charlotte, NC, Aug. 21–24, 2016.Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 12, 2016; final manuscript received February 7, 2017; published online March 24, 2017. Assoc. Editor: Yu-Tai Lee.

J. Mech. Des 139(5), 053401 (Mar 24, 2017) (13 pages) Paper No: MD-16-1636; doi: 10.1115/1.4036133 History: Received September 12, 2016; Revised February 07, 2017

Minimizing energy loss and improving system load capacity and compactness are important objectives for fluid power systems. Recent studies reveal that microtextured surfaces can reduce friction in full-film lubrication, and that asymmetric textures can reduce friction and increase normal force simultaneously. As an extension of these previous discoveries, we explore how enhanced texture design can maximize these objectives together. We design surface texture using a set of distinct parameterizations, ranging from simple to complex, to improve performance beyond what is possible for previously investigated texture geometries. Here, we consider a rotational tribo-rheometer configuration with a fixed textured bottom disk and a rotating top flat disk with controlled separation gap. To model Newtonian fluid flow, the Reynolds equation is formulated in cylindrical coordinates and solved using a pseudospectral method. Model assumptions include incompressibility, steady flow, constant viscosity, and a small gap height to disk radius ratio. Multi-objective optimization problems are solved using the epsilon-constraint method along with an interior-point (IP) nonlinear programming algorithm. The trade-off between competing objectives is quantified, revealing mechanisms of performance enhancement. Various geometries are explored and optimized, including symmetric and asymmetric circular dimples, and novel arbitrary continuous texture geometries represented using two-dimensional cubic spline interpolation. Shifting from simple dimpled textures to more general texture geometries resulted in significant simultaneous improvement in both performance metrics for full-film lubrication texture design. An important qualitative result is that textures resembling a spiral blade tend to improve performance for rotating contacts.

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Fig. 1

Textured surface design problem setup adapted from experiments conducted by Schuh and Ewoldt [17]. The periodic asymmetric dimpled textures used in the previous study are replaced here with arbitrary continuous texture shapes. (a) Front view of experimental setup and (b) top view of one textured surface periodic sector.

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Fig. 2

An example of texture height profile contours shown for a design domain sector (a) and for physical shape of a full disk (b). Darker regions correspond to lower surface levels (larger gap height).

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Fig. 3

Mesh points for (a) design representation in a coarse grid (6 × 6 nodes) and (b) flow simulation in a fine grid (26 × 26 nodes). The mesh for a reduced-dimension cubic spline texture shape design representation is shown on the left. This design mesh is much more coarse than the mesh on the right, which is required for accurate simulation. The surface geometry defined by the cubic spline is interpolated to determine all the height values at the fine mesh points required for simulation.

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Fig. 4

Alternative texture shape design representations. A cross-sectional view of each representation is shown in the top row, while a top view of each textured sector is shown in the bottom row. The gray area denotes the textured region (non-gray regions indicate unchanged flat surfaces). The top flat plates are rotating in the direction of the thick arrows, while the bottom textured surfaces are fixed. (a) Symmetric cylindrical texture, (b) asymmetric cylindrical texture, (c) asymmetric planar texture spanning full sector area, (d) arbitrary continuous texture with symmetry constraint, and (e) arbitrary continuous texture.

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Fig. 5

The ε-constraint method converts a multi-objective optimization problem to multiple single-objective optimization problems. For each scalarized problem, one objective is minimized while satisfying bound constraints on the other objectives.

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Fig. 6

Objective-function contours based on comprehensive sampling of the cylindrical texture design (symmetric and asymmetric textures). Trade-offs are apparent, and the Pareto sets are illustrated in the figures. Asymmetry improves performance capability, especially in terms of normal force. (a) ηa/η0, (b) −FN for symmetric textures, (c) ηa/η0, and (d) −FN for asymmetric textures.

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Fig. 7

Comparison of the Reynolds equation and the Navier–Stokes equation solutions in terms of the normalized apparent viscosity for the symmetric cylindrical textures as a function of depth

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Fig. 8

Geometry, shear stress, and pressure fields of optimized cylindrical texture designs in symmetric and asymmetric configurations. Symmetric texture Rt = 4 mm, h = 2.5 mm. Asymmetric texture Rt = 4 mm, β=3.6 deg. (a) −h, (b) τ, (c) p for symmetric textures, (d) −h, (e) τ, and (f) p for asymmetric textures.

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Fig. 9

Geometry and pressure field for asymmetric cylindrical textures with various angles (β). Six β angles are sampled within the range of inclination limits. (a)–(f) Geometric texture profile level sets and (g)–(l) pressure field level sets of corresponding β angles. (a) and (g) β = 0.9 deg, ηa/η0 = 0.942, FN = 0.281 N, (b) and (h) β = 1.8 deg, ηa/η0 = 0.920, FN = 0.573 N, (c) and (i) β = 3.6 deg, ηa/η0 = 0.904, FN = 0.755 N, (d) and (j) β = 7.2 deg, ηa/η0 = 0.880, FN = 0.614 N, (e) and (k) β = 10.8 deg, ηa/η0 = 0.854, FN = 0.449 N, (f) and (l) β = 14.4 deg, ηa/η0 = 0.829, FN = 0.333 N.

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Fig. 10

Geometry, shear stress, and pressure field of the surface texture with inclined plane spanning full sector area: (a) −h, (b) τ, and (c) p

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Fig. 11

Optimal designs for the cylindrical design exploration and the inclined plane spanning full sector area studies. The solid red stars in (a) are the Pareto set for the cylindrical texture identified from the contours of Figs. 6(c) and 6(d). In (b), the two objectives (ηa/η0 and FN) are plotted together as a function of β for the inclined plane design. The gray area indicates the region of suboptimal designs. (a) Optimal designs comparison and (b) β − ηa/η0, β − FN plots.

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Fig. 12

Optimal texturing of an arbitrary but symmetric surface approaches a flat plate. Symmetric texturing is unable to produce normal force. The optimal solution maximizes the gap everywhere to decrease the viscous shear load. (a) −h, (b) τ, and (c) p.

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Fig. 13

Geometry and pressure field of optimized surface textures with spline design representation (spline resolution N = 5). Asymmetry is permitted. Six designs are uniformly sampled from 27 designs in the Pareto set to illustrate trends. (a)–(f) Geometric texture profile level sets and (g)–(l) pressure field level sets. Note that these Pareto-optimal designs are located in Fig. 14 (square symbols). (a) and (g) design #4 (FN = 0.750 N, ηa/η0 = 0.299), (b) and (h) design #8 (FN = 1.750 N, ηa/η0 = 0.394), (c) and (i) design #12 (FN = 2.750 N, ηa/η0 = 0.469), (d) and (j) design #16 (FN = 3.753 N, ηa/η0 = 0.538), (e) and (k) design #20 (FN = 4.750 N, ηa/η0 = 0.607), (f) and (l) design #24 (FN = 5.752 N, ηa/η0 = 0.709).

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Fig. 14

Comparison of optimal designs in the objective-function space for all design studies presented in this article. Performance indices are improved significantly by increasing design flexibility via the texture surface representation.

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Fig. 15

Comparison of geometric texture profile level sets of optimal designs for N= 3, 4, 5, 6, 7 at FN = 3 N. As design resolution increases, the thickness of the bladelike feature becomes sharper, and a lower normalized apparent viscosity value can be achieved. (a) N = 3, ηa/η0 = 0.6015, (b) N = 4, ηa/η0 = 0.5160, (c) N = 5, ηa/η0 = 0.4857, (d) N = 6, ηa/η0 = 0.4439, and (e) N = 7, ηa/η0 = 0.4237.

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Fig. 16

Comparison of depth profiles: cross-sectional view ofoptimal designs, spline design representation cases with N= 3, 5, 7, and FN = 3 N. The horizontal axis indicates angular (θ) location within a sector, and the vertical axes correspond to texture elevation. Each subfigure corresponds to a different spline N. Positive thrust occurs when the opposing upper flat surface moves in the positive θ-direction.




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