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Model-based virtual surface texturing for concentrated conformal-contact lubrication D Zhu, T Nanbu, N Ren, Y Yasuda and Q J Wang Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 2010 224: 685 DOI: 10.1243/13506501JET739 The online version of this article can be found at: http://pij.sagepub.com/content/224/8/685

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SPECIAL ISSUE PAPER

685

Model-based virtual surface texturing for concentrated conformal-contact lubrication D Zhu1∗ , T Nanbu2 , N Ren3 , Y Yasuda2 , and Q J Wang3 1 State Key Laboratory of Tribology, Tsinghua University, Beijing, People’s Republic of China 2 Nissan Research Center, Nissan Motors, Kanagawa, Japan 3 Mechanical Engineering Department, Northwestern University, Evanston, Illinois, USA The manuscript was received on 21 September 2009 and was accepted after revision for publication on 4 March 2010. DOI: 10.1243/13506501JET739

Abstract: A model-based virtual texturing approach has been developed and applied to design, generate, ‘test’, and evaluate textured surfaces through numerical simulations. A series of studies on the numerical generation and performance evaluation of textured surfaces in a lubricated concentrated contact has been conducted, which includes (a) numerical generation of a large variety of textures considering possible geometric imperfections that exist in reality due to tooling design considerations and fabrication errors; (b) determination of texture depth, size, and area density; (c) texture distribution pattern selection; (d) bottom shape comparison and design optimization; (e) investigation of the influence of surface relative motion; (f ) prediction of performance deviation caused by texture shape imperfections; and (g) evaluation of the effect of originally machined roughness. The present study was conducted using the deterministic mixed elastohydrodynamic lubrication (EHL) model recently developed, modified, and validated, which appears to be useful for surface texture design based on comparative performance evaluation in a wide range of operating conditions. Keywords: surface design, design optimization, surface engineering, surface textures, virtual texturing, numerical simulation, elastohydrodynamic lubrication, mixed EHL, contact mechanics 1

INTRODUCTION

Design and optimization of surfaces are vital to the improvement of machine element performance, efficiency, and durability, because motion and power are transmitted in machine systems through surface contact, either lubricated or dry. It has been understood that texture design is an important part of surface engineering, and well-engineered textures may significantly enhance the hydrodynamic effect and reduce friction. Early efforts on textured surfaces used in metal forming were reported by Hector and Sheu [1]. More recently, a number of studies have been conducted through both experiments and numerical simulations in order to evaluate and optimize textured surfaces for tribological performance improvement in mechanical seals and a few other auto ∗ Corresponding

author: State Key Laboratory of Tribology,

Tsinghua University, Beijing 100084, People’s Republic of China. email: [email protected] JET739

parts (see references [2] to [19]). Early experimental studies were mainly on surfaces with round dimples of different sizes and depths produced by laser-beam processes (for example, see references [2] to [4], [6], and [10]). Micro-machining, blasting, metal-forming, and other techniques were also used, as reported in, for example, references [9], [13], and [17]. Concurrently, numerical analyses of various types were conducted to explore the characteristics of fluid flow influenced by textures/dimples [5, 12, 15, 16, 18, 19] and to develop model-based surface texture optimization approaches [14, 17]. Developing engineered surfaces demands an indepth and wide-scope understanding of contact mechanics and mixed lubrication, which is related to the type of contact, surface geometric features, materials, lubricants, and operation conditions. Evaluation and optimization of a surface texture design for a specific application typically require extensive investigations of surfaces with various textures under different operation conditions. Optimization of surface textures through experiments can be expensive Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

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D Zhu, T Nanbu, N Ren, Y Yasuda, and Q J Wang

and time-consuming, as it usually needs to go through a trial-and-error process, with repeated tests for screening a large number of combinations of surface features and testing parameters. There are many factors that may significantly influence the performance of textured surfaces. These may include depth, size, density, shape, distribution pattern, and imperfection of geometric features of the textures, and others; each may add an independent degree of freedom to surface design. On the other hand, computer-generated ‘virtual’ textures may precisely present the features of the desired surface topography and support a modelbased numerical tool capable of predicting tribological performance through contact and mixed lubrication analyses. However, virtually texturing surfaces for tribological applications is a complicated task. Besides the additional degrees of freedom added by texture shape, depth, size, density, and distribution patterns to the surface creation, operating conditions have to be fully simulated as well. In engineering practice, shallow dimples and grooves, typically not more than a few microns, are usually preferred for maximal lubrication enhancement without incurring excessive fatigue stress raisers. The depth of dimples or grooves is usually designed to be much smaller than the lateral size. The Reynolds equation, therefore, is still applicable for the lubrication analysis of most textured surfaces. The theory of hydrodynamic lubrication and the practical experience with step bearings, grooved bearings, and seals have indicated that the effect of possible turbulence caused by the shallow surface textures is often negligible. It is believed that a robust mixed elastohydrodynamic lubrication (EHL) model associated with a numerical surface texture generator should be a proper virtual surface texturing tool. In the present study, a deterministic mixed EHL model, recently developed by Hu and Zhu [20, 21] and modified by Liu et al. [22, 23] and Zhu [24], is employed as the numerical ‘tester’ to evaluate the performance of different surfaces. The virtual texturing technique, described in reference [14] and already applied in references [17], [25], and [26], is further improved to take into account the effects of possible texture imperfections, original machined roughness, and relative motion of textured surfaces. This is a continuation of a series of studies reported in references [25] and [26]. This article summarizes the major results of this series of studies, while the main focus is on the new results for the effects of texture shape imperfections and original machining marks on lubrication. 2 VIRTUAL TEXTURING TECHNOLOGY Virtual texturing technology contains two key elements: virtual texture generation and performance Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

Fig. 1 Virtual texturing procedure and examples of textures. (a) Model-based virtual surface texturing [14]. (b) Texture examples. From top left, sinusoidal grooves of the same orientations, sinusoidal grooves of opposite orientations, honeycomb dimples, short grooves in a triangular distribution combined with original machined roughness, fishbone dimples, and fishbone grooves

and life evaluation through mixed EHL analysis. Figure 1(a) presents the diagram for this concept. Detailed description of virtual texturing can be found in reference [14], but a couple of key issues are repeated here for clarity.

2.1 Virtual texture generation The texture on a surface is typically a periodic extension of a single geometric feature. In most cases, therefore, surface texture generation consists of two steps: (a) the numerical description of the single geometric feature, which may be a dimple or groove or other geometric shape; (b) a procedure to automatically duplicate the feature following a certain pattern, which may be called ‘numerical patterning’. A computer program has been developed following these two steps, and a large variety of surface textures with different geometric shapes and distribution patterns can be generated. Several typical examples can JET739

Model-based virtual surface texturing for concentrated conformal-contact lubrication

be found in Fig. 1(b). This virtual texture generation technology has been successfully employed in references [14], [17], [25], and [26]. In the present study, this virtual texture generation technique is further improved to consider possible geometric shape imperfections due to practical tooling design preferences and fabrication errors, as well as the existence of original surface roughness. These are very practical concerns that must be taken into account, as various geometric imperfections are unavoidable, which are often of the same order of magnitude as the desired shallow textures. Whether these imperfections would cause noticeable performance deviation certainly deserves research attention. Figure 1(b) shows an example of a texture generated on originally machined rough surface. Detailed description of other geometric imperfections will be given in the following sections. 2.2

Mixed EHL modelling

This study uses the full numerical solution model for the mixed EHL, originally developed by Hu and Zhu [20, 21] and continuously modified by Liu et al. [22, 23], Zhu [24], and others. Details of the model have been reported in previous publications. Note that the model system is based on the full numerical solution of transient mixed EHL, using the transient Reynolds equation, as involvement of moving rough surfaces, machined or textured, makes the lubrication time dependent because the film thickness now varies with the moving surface topography. Some recent improvements of this model include the following. 1. The effects of differential schemes and computational mesh density have been investigated, and numerical algorithms optimized accordingly (see references [22] and [24]). 2. A progressive mesh densification method has been developed to ensure the numerical accuracy while significantly accelerating the iterative solution process (see reference [24]). 3. A discrete convolution fast Fourier transfer (FFT) approach, originally developed by Liu et al. [27], has been adopted in the mixed EHL solution by Wang et al. [28] and others, so that the surface elastic deformation calculation (which is a dominant part of total computation) has been significantly accelerated. 4. Traditionally, line-contact EHL problems can be simplified as two-dimensional (2D) under the smooth surface assumption. However, for machined/textured rough surfaces, the problems can no longer be considered as 2D, because the surface topography, possible asperity contacts, local lubricant flows, and pressure/film thickness distriJET739

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butions are usually all 3D. A 3D line-contact mixed EHL model has been developed by Ren et al. [29] as an important addition to the present model approach. 5. Model validation cases in a wide range of operating conditions have been continuously analysed and reported (for example, references [23], [24], [28], and [29]). Figure 2 presents one of such cases from reference [23] as an example, in which a textured surface with transverse multi-ridges runs through a circular EHL contact, and the numerical solutions are compared directly with optical interferometry results from reference [30]. Good agreement has been found (see reference [23] for more details). This evidently indicates that the present mixed EHL model is adequate for virtual texturing studies. Note that inter-asperity cavitation is considered in the analyses by applying the commonly used Reynolds boundary condition throughout the entire solution domain for possible cavitation that may take place not only on the outlet side of the Hertzian contact but also at the outlet side of the micro-asperity contact. It is believed that cavitation may not significantly affect the EHL film thickness, which is mainly determined by the entraining action in the inlet zone. 3

SIMULATION RESULTS AND DISCUSSION

The interface in the studied system is formed between an internal cylindrical surface and an ellipsoid, as illustrated in Fig. 3. The input data, such as material properties, operating conditions, and contact geometry, have been reported in detail in references [25] and [26], and some key parameters are repeated here for clarity. The radii of curvature of body 1 (made of steel) in the motion direction (the X direction) and the Y direction are 21.5 and 700 mm, respectively. The internal cylindrical surface of body 2 (aluminium alloy) has a negative radius of curvature, −22.5 mm. A mineral oil is used as a lubricant, and the lubricant properties are density at room temperature, ρ0 = 0.82 g/cm3 ; dynamic viscosity at inlet, η0 = 0.013 35 Pa s; and pressure– viscosity coefficient, α = 12.63/GPa. The surface of body 1 is numerically textured, whereas the surface of body 2 is assumed to be smooth (unless otherwise noted). Two speed conditions were used for the cases presented in this study. The first is to have U1 = 5 m/s and U2 = −1 m/s, so that the rolling speed is U = 2 m/s and the slide-to-roll ratio is S = −3. The other is a simple sliding condition at a rolling speed U = 3 m/s, with the textured surface moving and the smooth surface being stationary. For each group of cases, the speed condition will be specified below. The normal applied load is w = 196 N. The corresponding semi-axes of the Hertzian Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

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Fig. 2

A model validation case: comparison of mixed EHL simulation results with optical interferometry data by Kaneta et al. (from reference [23])

U1 700

Steel

b =1297 micron

21.5 a =992 micron U2

-22.5 Aluminum alloy

Fig. 3 The concentrated conformal system studied

contact ellipse are a = 0.992 mm and b = 1.297 mm, respectively, and the maximum Hertzian pressure is about Ph = 0.073 GPa. Because the Hertzian pressure is quite low and the contact area relatively large, the interface is named as a ‘concentrated conformal contact’. The average film thickness over a circular region at the centre of the normalized Hertzian contact zone, whose radius is two-thirds of the normalized Hertzian radius, is used for the results shown in Figs 4 to 6. With Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

this method, films from the texture grooves or dimples in this region are included while calculating the average. However, the results are comparable because the texture densities and depths in each group are the same, and the effect of different bottom shapes is small. The minimum central film thickness is used for the rest of this study. It is taken at the lowest bank clearance along the Y = 0 cross-section where the average film thickness is minimal. When machined roughness presents, this value is the average at the lowest bank clearance along the Y = 0 cross-section. In either case, the film in the textures is not included. Moreover, operational conditions may significantly affect the performance of textures, so the results obtained from the analysed cases may not be generally applicable to some other cases under different conditions. The presented cases are for the specific condition set targeting at a specific application, but they are also examples demonstrating the simulationbased virtual texturing approach, which is generally applicable for performance evaluation of different JET739


Fig. 4

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Effect of texture distribution patterns on film thickness. The central film thickness of smooth surfaces is used as the reference. U1 = 5 m/s, U2 = −1 m/s, and U = 2 m/s

0.0016

Film thickness (H/a)

0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 R

U

T1

T2

T3

W1

W2

W3

W4

Bottom Geomtry

Fig. 6 Fig. 5

Effect of bottom shapes on film thickness. Two film enhancement mechanisms, the step bearing effect and the wedge effect, are indicated, and the film-pressure distributions for T shapes are compared. U1 = 5 m/s, U2 = −1 m/s, and U = 2 m/s

surface finish processes/textures in wide ranges of operating conditions. The current work tries to tackle this complicated problem by providing relative comparisons. Film thickness is chosen to be the criterion in the comparisons. It is believed that film thickness is most representative, and enhanced film thickness can help prevent asperity contact, reduce friction, and thus avoid many unwanted surface and interface problems. JET739

3.1

Effect of bottom shapes on the central film thickness. W 2, W 4, and T 3 seem to be the best shapes. R is also desirable because of its simplicity and relatively good performance. U1 = 5 m/s, U2 = −1 m/s, and U = 2 m/s. The broken line shows the reference film thickness of smooth surface lubrication

Determinations of dimple/groove depth, size, and density

Dimple depth, d, is a critical parameter, which may be determined based on experiments and/or the theory of hydrodynamic lubrication [31] with respect to the projected operating film thickness. Optimized dimple depth is often correlated to the expected film thickness. Many studies suggested the use of a reasonably small depth. Kovalchenko et al. [10], Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

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for example, conducted a group of experiments on the frictional behaviour of disc surfaces with circular dimples made with a few different depths, density, and diameters, using different rotational speeds and two lubricants. Their results appear to favour the shallowest dimples of about 4 µm. Wang and Zhu [14] carried out an investigation at a few different speeds and loads. It was found that the depths less than 0.2–0.3 per cent of the Hertzian radius (typically only a couple of microns or less) may yield thicker films, and deep dimples, on the other hand, may have a considerable negative impact to the film formation. Moreover, deep textures may greatly increase the risk of surface failures such as spalling and pitting due to contact fatigue. Nanbu et al. [26] conducted both full numerical simulations and simplified estimates with the same set of input data as those in the present study. The optimized depth was found to be about 1–2 µm. Because possible running-in and wear may reduce the depth, a depth of 3 µm was chosen in reference [26] for most cases analysed. This depth will also be used in the present study. Another method to estimate the favourable dimple depth is to use the inlet suction mechanism recently reported in references [15] and [16]. Its basic results and conclusions appear to be consistent with those described above. The effects of dimple/groove size and density were also investigated in the present series of studies. Results and conclusions were found to be in agreement with those already reported in reference [14]. Basically, very small geometric features are not preferred. Reasonably large-sized dimples/grooves may perform better as long as they are still considerably smaller than the size of the Hertzian contact zone; thus, there are still a good number of dimples/grooves distributed within the contact area. It was also observed that a small area density of about 5–10 per cent is often preferred, and very dense textures beyond 20–30 per cent may cause a collapse of the lubricant film.

3.2 Texture distribution pattern selection Five groups of texture distribution patterns, including fishbone with grooves, fishbone with dimples, sinusoidal with grooves, triangular, and honeycombs with dimples and grooves, are generated. Their lubrication performance is numerically evaluated for pattern screening and understanding of the effects of texture direction, shape orientation, and aspect ratio on lubrication enhancement. Several texture examples are shown in Fig. 1(a). The results of the numerical studies of the elliptic contact, based on the geometry and the operating conditions used in reference [25] and the present work, can be summarized in Fig. 4, which leads to the following observations. Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

1. Narrow short grooves perpendicular to the motion direction appear to be the best choice among all the samples studied. A sinusoidal wave with a small wavelength/amplitude ratio, propagating along the motion direction, may also be a good selection. 2. The texture direction effect is investigated based on film-thickness results of fishbone patterns, sine waves, and honeycomb and triangular patterns. All results indicate that the texture direction, either face to face or face to back, only has a negligibly small influence on the lubrication effectiveness. 3. The texture orientation angle strongly affects the film thickness. Smaller orientation angles are preferred for getting thicker films. 4. Texture aspect ratio in terms of width/length is inversely related to the film thickness. Smaller aspect ratios are preferred for EHL film formation. 3.3

Bottom shape comparison and relative motion utilization

Three groups of bottom geometric shapes – U and R; T1, T2, and T3; and W1, W2, W3, and W4 – are numerically generated and shown in Fig. 5. The surfaces of these shapes are assumed to be smooth. In order to focus on the bottom shape effect, the texture distributions are all arranged in an equilateral triangle pattern. Note that each W shape can be considered as a combination of two T shapes, T2 and T3. W1 and W2 are similar, but there is a raised flat area of 85 µm width between the two T’s inW2, whereas the triangular summit in W1 is below the top surface. Likewise, W3 and W4 are constructed in a similar way, except that W3 has a flat bottom of 85 µm width. The results from the bottom shape effect study, summarized in Fig. 6, clearly indicate that the flat bottom R shape, the T3 shape, and the W2 and W4 with doubled triangles are preferred for lubrication enhancement. Faster moving textured surface should bring additional flow into the interface and result in film thickness enhancement. This suggests that textures be made on the faster moving surface. Note that the ‘moving surface’ should be identified based on the relative motion of the texture that the lubrication region experiences ‘moving’ textures. 3.4

Both surfaces textured

Twenty cases with different combinations of textured surfaces have been numerically analysed in order to study whether it is necessary to texture both surfaces in the EHL contacts. The moving surface is ‘textured’ with difference shapes, whereas the mating stationary surface is either smooth or grooved and may resemble machining marks from a manufacturing process. The film thickness for smooth surfaces is also included as a reference for comparison. The results obtained are JET739


Stationary Moving Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case

1: 2: 3: 4: 5: 6: 7: 8 9: 10: 11: 12: 13: 14: 15: 16: 17 18: 19: 20:

Case 6

Smooth Smooth Smooth Smooth R Groove R Groove R Groove R Groove Sine Groove Sine Groove Sine Groove Sine Groove T3 Groove T3 Groove T3 Groove T3 Groove W4 Groove W4 Groove W4 Groove W4 Groove

Smooth R Texture T3 Texture W4 Texture Smooth R Groove T3 Groove W4 Groove Smooth R Texture T3 Texture W4 Texture Smooth R Texture T3 Texture W4 Texture Smooth R Texture T3 Texture W4 Texture

Case 12

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h/a 2.50E-03

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10 11 12 13 14 15 16 17 18 19 20

Case

Case 18

Case 19

Case 20

Transient average film thickness and combined roughness for case 19.

Fig. 7

Central film thickness comparison for cases with both surfaces textured. Simple sliding with U = 3 m/s. Several film distribution snapshots are presented, and the transient average film thickness and combined roughness for Case 19 is illustrated

illustrated in Fig. 7. The major input parameters, such as the contact geometry, the materials, and the load, are the same as those mentioned before, except that Surface 1 is stationary and Surface 2 moving at 6 m/s, so that the rolling speed is 3 m/s. The results suggest that not all surface combinations help enhance film thickness. T 3 and W 4 still show advantages over other textures. Furthermore, it seems to be unnecessary to texture both surfaces. For the purpose of fabrication cost reduction, one can texture only the moving surface while keeping the stationary surface un-textured. The performance may still be satisfactory, as shown by Cases 3 and 4 in Fig. 7. 3.5

Performance deviation due to shape imperfections

In engineering reality, the actual geometry of textures might deviate from the theoretically suggested shapes due to several reasons, such as tooling design preference, fabrication error, and possible elastic restoration, after the fabrication process is completed. Generally, the imperfections are unavoidable in practice. Sometimes, the geometric deviations may be of the same order of magnitude as the depth or the size of JET739

designed textures, which may cause noticeable change of the textured surface performance. Some common types of geometric imperfection have been studied in the present work, and the results are reported in the following. 3.5.1

Triangular valley bottom shifting

T3 textures described above appear to be advantageous in lubrication enhancement. However, it is not practical to make the ideal shape owing to difficulties associated with the tooling design and fabrication process. From the manufacturing point of view, it is much better if the downstream vertical edge can be allowed to tilt slightly. This part of the study aims to determine how much of the bottom shift, X , shown in Fig. 8, the T3 geometry can tolerate without sacrificing its performance. In the analysed cases, rectangular grooves are distributed in a triangular pattern, and the groove density is about 10 per cent. Surface 1 is textured whereas Surface 2 is smooth. The bottom shift is specified by X , as illustrated in Fig. 8. When X = 0, it is a T3 shape and the thickest film is obtained. No significant film thickness reduction is observed if X < 10–20 per cent of the groove width, L. This, in Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

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Motion of textured surface Depth x

X=0, T3

X= L, T2

L

0.35(2a)~700

0.35b~450 L= a/10 ~95 µm

Film thickness (h/a)

0.0016

Density =10% Surface 2 smooth U1 = 5m/s, U2 =-1m/s U= 2 m/s Fig. 8

0.0012 0.0008 0.0004 0 0

20

40 60 X Position (m icron)

80

100

T -shaped imperfection due to valley bottom shifting. Practically, x = 0 (T3) and x = L (T2) are not preferred owing to difficulties with tooling, but they are not necessary either

Fig. 9

T -shaped bottom imperfections due to possible curvatures

fact, provides a range of bottom deviation tolerance, which may be a useful reference for design and fabrication. Note that, on the other hand, it is a T2 shape if X = L. Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

3.5.2

Triangular shape edge imperfection

It is difficult to make a perfectly straight edge for the T3 shape, and both positive and negative curvatures JET739


may occur, as shown in Fig. 9, when different fabrication methods are used. In this group of cases analysed and presented in Fig. 9, Surface 1 is textured at an area density of 5.2 per cent, and a simple sliding of U1 = 6 m/s applies. The results show that a reasonably small positive curvature (concave) helps increase the film thickness. Small negative curvature

(convex, caused possibly by elastic restoration) might slightly reduce the film thickness. In general, the influence of edge curvature in either direction appears to be quite limited, as long as |R0 /L| is not smaller than 10–15 per cent. This information may be useful for tooling design.

3.5.3

Fig. 10

R-shaped imperfection due to fillet. Small R0 is preferred but R0 = 0 is not practical

Fig. 11 JET739

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Rectangular bottom shape imperfection due to fillet

Rectangular bottom shape (R shape) can hardly be made exact by either the mechanical techniques or the laser-beam process, and edge fillets with a radius, R0 , usually exist, as shown in Fig. 10. Similar to the conditions mentioned in the last section, the short groove-shaped dimples are distributed in a triangular pattern with an area density of 5.2 per cent, and the simple sliding condition of U1 = 6 m/s applies. Results in Fig. 10 suggest that, in general, fillets in the given direction reduce film thickness. However, the reduction is quite limited, less than 10 per cent in the range of the data studied. Such film thickness reduction may be partially due to the reduction of the effective dimple volume.

W -shaped bottom imperfection due to possible curvature Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

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Fig. 12

Machined surfaces. Surface A: Rq = 0.11 µm, Surface B: Rq = 0.29 µm, Surface C: Rq = 0.47 µm, and Surface D: Rq = 0.08 µm

Film thickness (h/a)

2.50E-03

2.00E-03

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1.00E-03

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0.00E+00 1

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Case Case #: Case 1: Case 2: Case 3: Case 4: Case 5: Case 6: Case 7: Case 8: Case 9: Case 10: Case 11: Case 12:

Surface 1 (stationary): Smooth Bearing Smooth Bearing Bearing: Surface A Bearing: Surface A Bearing: Surface B Bearing: Surface B Bearing: Surface A Bearing: Surface A Smooth Bearing Bearing: Surface A Bearing: Surface B Smooth Bearing

Case 6

Surface 2 (moving): T3 Dimples combined with smooth surface T3 Dimples combined with Surface C T3 Dimples combined with Surface C T3 Dimples combined with smooth T3 Dimples combined with Surface C T3 Dimples combined with smooth Surface C with no dimples Surface D with no dimples T3 Dimples combined with Surface D T3 Dimples combined with Surface D T3 Dimples combined with Surface D Smooth surface with no dimples

Case 10

Fig. 13 Textures on machined surfaces. Surface A: Rq = 0.11 µm, Surface B: Rq = 0.29 µm, Surface C: Rq = 0.47 µm, and Surface D: Rq = 0.08 µm. Simple sliding with U = 3.0 m/s Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

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3.5.4 W-shaped bottom imperfection Similarly, it is difficult to make a perfectly flat bottom for the W shapes. Both positive and negative curvatures may occur, as shown in Fig. 11, when different fabrication methods are used. All the conditions are the same as those mentioned above. The results shown in Fig. 11 indicate that the flat (straight line) bottom shape is the best choice. Small curvature (1/R < 0.001) may be allowed. Negative curvature (convex) is worse than a positive curvature (concave). This may provide some insights to tooling design and fabrication process. 3.6

Effect of machined roughness

Textures have to be made on top of machined surfaces because an ideally smooth surface does not exist in reality. It is always a key question in various engineering applications how the surfaces should be prepared before textures are made. Therefore, it is necessary to investigate the combined effects of the machined roughness and fabricated textures on lubrication characteristics. In this part of the study, four types of machined surfaces, Surfaces A, B, C, and D, as shown in Fig. 12, are the available choices as the original surface to be combined with a selected texture to form Surface 1 or 2 in each analysed case. Totally 12 cases have been numerically studied. The case arrangements and obtained simulation results are summarized in Fig. 13. A simple sliding condition of U1 = 0 and U2 = 6 m/s is employed here. In general, selected T3-shaped dimples and machined roughness both may enhance the film thickness. Compared with smooth surfaces, machined roughness may increase the film thickness slightly, whereas the selected dimples may increase the film thickness significantly. It is better to have a smoother machined roughness (e.g. Surface D) combined with textures for Surface 2 and to use a smoother machined surface (e.g. Surface A) as the mating stationary surface if the moving surface is T3 dimples combined with another machined surface. Realistically, therefore, surface selection in Case 10 (Surface A for stationary bearing and Surface D combined with T3 dimples for moving journal) is recommended for the given operating conditions. Note that the roughness values are used to indicate the deviations of the machined surfaces from the smooth one. Although other surface characteristics are reflected in the digitized topographic data used in the analyses, no conclusions are drawn with respect to surface topography because only four surfaces were employed. 4

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possible imperfections, original surface finish, contact type and geometry, materials and the lubricant, and operating conditions. Each factor might significantly affect the contact and lubrication performance under certain conditions. In the present study, most factors mentioned above have been investigated and recommendations are made for texture design under the given conditions. In the range studied in this series of work, the results suggested the following details. 1. Dimple depth may be determined based on experiments and the theory of hydrodynamic lubrication. Dimple depth optimization is usually related to the expected film thickness. 2. Many distribution patterns were studied, and narrow short grooves perpendicular to the motion direction and sinusoidal wave with a small wavelength/amplitude ratio propagating along the motion direction seem to be among the best choices. 3. Several bottom shapes were numerically tested, and those including a micro-step bearing and an effective micro-wedge bearing are preferred for lubrication enhancement. 4. Real texture shapes may deviate from the theoretically suggested geometry due to tooling design preferences, fabrication errors, and elastic restoration. The investigation on triangular texture bottom shapes reveals that about 10–20 per cent of valley bottom offset can be allowed. 5. Rougher machined surface may reduce the film thickness enhancement effect of dimples. It is important to note that all the recommendations based on the virtual texturing simulation results are pertaining to the present application in this set of specific concentrated conformal contact and operating conditions, although the insights gained from the present study may be useful for some other applications. It is also important that, while some selected textures may greatly increase the EHL film thickness and thus improve the performance and efficiency, some other textures may evidently cause a considerable decrease in the film thickness. It is not true that all the textures can enhance the lubrication. Texture performance depends on operating conditions. A specific texture may perform well under one condition but may no longer work when the condition is changed. Therefore, each texture must be carefully designed, evaluated, and tested under specific conditions before its application. Texture optimization is a complicated system problem, and a well-developed model-based analysis tool is certainly needed.

CONCLUSIONS ACKNOWLEDGEMENT

Surface texturing is a complicated system problem involving many factors, such as texture geometric shape, depth, size, density, distribution pattern, JET739

The authors thank Nissan Motors for supporting the present work and publication of the present article. Proc. IMechE Vol. 224 Part J: J. Engineering Tribology

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