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Directional friction surfaces through asymmetrically shaped dimpled surfaces patterned using inclined flat end milling
Tribology International 91 (2015) 67–73
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Tribology International journal homepage: www.elsevier.com/locate/triboint
Directional friction surfaces through asymmetrically shaped dimpled surfaces patterned using inclined flat end milling Jesus Resendiz, Eldon Graham, Philip Egberts n, Simon S. Park Micro Engineering Dynamics and Automation Laboratory (MEDAL), Department of Mechanical & Manufacturing Engineering, University of Calgary, 40 Research Place NW, Calgary, Alberta, Canada T2L 1Y6
art ic l e i nf o
a b s t r a c t
Article history: Received 4 March 2015 Received in revised form 28 May 2015 Accepted 19 June 2015 Available online 29 June 2015
In this study, directional friction effects by creating asymmetrically shaped dimpled surfaces on an aluminum workpiece were investigated. The surfaces were created using the inclined micro-flat end milling process. Inclined micro-milling forces were modeled, and subsequent comparisons with the measured forces have provided validation. These simulations also showed that the flat end mill used to produce these dimpled surfaces was not symmetric. Tribological characterization of the friction properties of the surface using reciprocating tribometer and a hemispherical ruby counter surface indicated that these asymmetrically shaped dimples lowered the overall friction coefficients measured under both dry and lubricated sliding conditions. Moreover, the results also demonstrated a sliding direction dependent response, in terms of the measured friction coefficients. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Micro-patterns Functional surfaces Micro-flat end milling Friction
1. Introduction Functional surfaces play an important role in the behavior of engineering parts, such as those in mechanics, electronics, information technology, energy, optics, biology, and biomimetics [1]. Reduction of friction depends on many factors: one of the important factors is the topography of the rubbing interfaces [2]. For example, patterned surfaces are one mechanism by which the lifetime of hip replacements can be extended [3]. In more conventional engineering mechanical systems, such as in automotive lubrication, functional surfaces in the form of microdimples have been shown to reduce friction between mechanical components through the following mechanisms: debris caused by mechanical wear of the sliding surfaces can be trapped by the textured surface [1,4]; the textured patterns can act as lubricant reservoirs, allowing for a faster transition to the elastohydrodynamic lubrication regime as the device is switched on [5]; and, textured surfaces can also influence the hydrodynamic pressure between surfaces, which can result in increased load carrying capacity [4,6,7]. Since uniformly shaped surface features can be difficult to produce, many researchers have observed anisotropic frictional effects that depend upon the orientation of surface features to the n
Corresponding author at: 40 Research Place NW, Calgary AB, T2L 1Y6. E-mail addresses: [email protected] (J. Resendiz), [email protected] (E. Graham), [email protected] (P. Egberts), [email protected] (S.S. Park). http://dx.doi.org/10.1016/j.triboint.2015.06.025 0301-679X/& 2015 Elsevier Ltd. All rights reserved.
sliding direction [8]. Depending upon the type of surface structures, frictional performance is often superior in a specific direction [4,9]. In fact, anisotropic frictional effects arise naturally in many materials, such as wood and composites, due to the material structure and surface roughness [8]. Compared to other surface texturing methods, such as wet or dry etchings, abrasive jet machining and laser processes, inclined micro-milling can be an efficient and cost-effective method to fabricate micro-dimples, because complex systems are not necessary. Inclined micro-milling is very precise and does not have high energy consumption, and a mask is not required. The micromilling technique significantly reduces the time needed to fabricate dimpled surfaces by creating a row of dimples in a single pass of the cutter. Many other machining methods are not efficient by comparison, as individual dimples are made through repeated horizontal and vertical movements of the cutting tool; thus, pattern surfaces from inclined micro-milling exhibit improved tribological properties [10]. Determination of the optimal structure that can influence the friction response of a mechanical system is of particular interest. Such surfaces have been realized through ball end milling [11] and fly cutting [12]. Advantages of micro-milling producing microtextured surfaces include high material removal rates, accurate surface finishes, and few restrictions on workpiece materials [13]. It has also been shown that micro-milling can be used to produce a variety of different surface structures by altering the cutting technique [14]. Micro-milling thus represents a very flexible method, and, with the right combination of cutting technique
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and tool geometry, a wide variety of surface structures can be developed. However, care must be taken when using micromilling to pattern surfaces, as in machining patterns, oscillations of cutters while rotating, cutting tool wear or breakage, tool deflections, non-uniformity of cutting conditions, varying rigidity of the workpiece or clamping system, and abrupt movements of the workpiece while texturing can detrimentally influence the resulting surface structure [15]. Predictive modeling of the machining forces is one mechanism by which of these disadvantages can be reduced, as several of these challenges can be identified beforehand, such as cutting tool wear or breakage and tool deflections. Furthermore, comparison of measured machining forces with those predicted by the model can be used to identify issues with patterning the surface, such as issues with uniform cutting, oscillations in the cutter, or tool wear. The performance of textured surfaces depends upon the geometry of the surface patterns. It is, therefore, essential to understand how different machining parameters affect the resulting topographic structure. In this paper, the cutting forces are evaluated to determine the effect of machining parameters on tool longevity and efficiency, as well as patterning performance and efficiency. The surface topography generated by a flat end mill on aluminum alloy Al6061 is characterized to ensure the machining simulations match experimental measurements. Finally, the tribological performance of anisotropically shaped micro-dimples is evaluated and shown to have sliding direction dependent friction coefficients. An understanding of the basic relationship between these parameters allows manufacturers to optimize the tool path and surface features and minimize, tool wear and deflection.
2. Methods
the stage using a Keyence Laser Displacement Sensor (LK-G3001) in relation to the number of steps counted during the translation of the stage. Samples were produced by fixing the Al6061 workpiece to a piezoelectric table dynamometer (Kistler 9256C), allowing for future measurements of cutting and friction forces. Before producing dimples, the surface of the aluminum workpiece was flattened by milling the top layer of the surface with the spindle positioned so that its long axis was perpendicular to the workpiece surface normal. To ensure a sufficient supply of oil for lubricated surfaces during friction testing, a small depression of about 2 mm was machined onto the surface of half of the workpiece. This depression ensured that the lubricated and unlubricated surfaces had the exact same surface normal in subsequent friction testing. Following the surface planning and milling of the oil reservoir, the surfaces were polished using a P800 grit sandpaper to remove machining marks and reduce surface roughness. The surface roughness was measured over a 1 1 mm2 area to be less than 0.11 70.02 mm (Mitutoyo SJ-201P). To measure cutting during dimple fabrication and friction forces, analog signals from the table dynamometer were amplified by a factor of 10 (Kistler Charge Amplifier 5010) and digitally recorded (National Instruments BNC-2110) at a sampling rate of 1 kHz. Dimpled surfaces were produced by fast translation of the sample workpiece while the end mill, now inclined at angle of 601 to the surface normal, was close enough for the flutes to cut the surface. A flat end mill (PMTs TS-2-0350-S) containing two flutes and with a diameter of 889.0 μm was used, producing dimples of approximately asymmetrically shaped dimples that were approximately 30 mm deep and 300 mm in the largest lateral dimension. Further details of the shape of the resulting surface texture are discussed in the next section.
2.1. Machining of patterned surfaces Flat and dimpled surfaces were machined using a home-built computer numerical control (CNC) micro-milling system. This system is graphically depicted in Fig. 1(a) and photographed in Fig. 1(b). The CNC was mounted and secured on a vibration isolation table to insulate the machining system from the ground. An electric spindle (NSK Astro-E 800Z) was mounted onto a bracket that allowed the spindle to rotate at an inclination angle relative to the sample surface and to be secured during machining. Translation of the workpiece below the spindle during machining and friction testing was achieved by mounting the workpiece on linear precision stages (Parker Daedal 10600). These linear precision stages were actuated with stepper motors that were computer controlled (National Instruments PXI-1042Q). Calibration of the stepper motors was made by measuring the real displacement of
2.2. Modeling of inclined flat end milling forces Conventional cutting force models for flat end mills can be modified to predict forces for inclined flat end milling. Three force components on the milling cutter must be considered to account for the effects of spindle inclination. Inclined cutting of dimples with a flat end mill is periodic and not continuous as in upright milling, and each flute enters the workpiece surface with a certain frequency. Since the tool geometry of a flat end mill allows for uniquely shaped dimple geometries, an investigation into how cutting forces are affected is warranted. Using the conventional force model, cutting forces can be identified while the end mill is inclined in local x'–y'–z' coordinates. Afterwards, they can be
Fig. 1. (a) Schematic of the machining system used. The flat end mill is tilted with respect to the surface normal of the workpiece to produce the dimpled surface. (b) Photograph of the end mill setup used to produce the dimpled surfaces. The spindle in this case is at an inclination angle (γ) of 601 with a flat end mill attached.
J. Resendiz et al. / Tribology International 91 (2015) 67–73
z’
z R
ϒ
z’
f Aluminum Workpiece
R
φ
R
x’
x’
θ=0
x
y’
y’ φ
y
n
ϒ
n
z’ ϒ
69
f
x’
α (ϒ)
z’(k) R
d
d
Fig. 2. Analytic model of a flat end mill. (a) The tool is inclined at angle γ and helix angle β. When the tool moves through the workpiece surface, each flute successively cuts a dimple into the material at cutting depth d. (b) A cylindrical micro-end mill can be modeled as rotating element with spindle speed n (rev/min) that moves with feed rate f (mm/s), and the position of a point on the cutting edges can be described in x'–y'–z' coordinates. (c) Knowing a point with distance R from the bottom of the end mill and the top of the end mill at given time t, it is possible to transform this point to global x–y–z coordinates by relating to the cutting depth, inclination of the tool, and feed rate.
Capped End Mill with a Ruby Half-Sphere
Aluminum 6061 workpiece
Wear Groove Caused by Friction Reciprocation
Laser Displacement Sensor
Spindle at 0° Inclination
Table Dynamometer
Fig. 3. Photograph of friction measurement apparatus/tribometer. A 6 mm ruby ball is attached at the end of an end mill held stationary, while the workpiece, attached to a table dynamometer (a 3-axis force sensor), is moved in a reciprocating motion. A laser displacement sensor measures the stage movement.
transformed back through the inclination angle to the global x–y–z coordinate system. The conventional mechanistic force model for shearing dominant cutting for a flat end mill determines forces by calculating the chip thickness and identifying cutting coefficients [16]. The conventional force model for standard upright helical end mills describes three force components (tangential, radial, and axial). The general formula for the chip thickness h of a flat end mill is given by h ¼ f t sin ðϕÞ
ð1Þ
where ft is the feed rate (mm/flute), and ϕ is the tool rotation angle adjusted for the number of flutes and position along the cutting edge. End mills experience a resultant force comprised of three components in the radial, Fr, tangential, Ft, and axial, Fa, directions. For shearing dominant cutting [16], the elemental component of each can be expressed as: dF r ¼ K rc hdz0 þ K re dz0
ð2Þ
dF t ¼ K tc hdz0 þK te dz0
ð3Þ
dF a ¼ K ac hdz0 þ K ae dz0
ð4Þ
where Krc, Ktc, Kac, Kre, Kte and Kae are the cutting and edge coefficients in each direction, respectively, and dz' is the differential axial height of the cutter.
Fig. 4. Measured friction coefficient versus cycle number for a flat, oil-lubricated surface. One hundred reciprocation cycles were recorded at an applied load of 5 N on the Al6061 workpiece. The green square shows the region from which the steady-state friction coefficient was determined, which approximately corresponds to friction coefficients recorded from cycle numbers 25–90.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The cutting coefficients depend on the tool geometry and workpiece material and are different for each cutting tool and workpiece combination. These parameters must be identified experimentally from cutting tests. Surface topography can be predicted analytically by relating tool geometry and machining parameters to the workpiece surface. As shown in Fig. 2, a cylindrical micro-end mill can be modeled as rotating with spindle speed n (rev/min) and moved at feed rate f (mm/s). The tool is inclined at angle γ and has radius R, N number of flutes, and helix angle β. As the tool moves over the workpiece surface, each flute successively cuts a dimple into the material at maximum cutting depth d. The angular direction of feed θ is defined from the x-axis. For this study, the spindle was inclined about the y-axis in the same direction as the tool feed or x-direction (θ ¼ 0). The equations that relate an inclined ball end mill with the position of the cutting edge to a flat workpiece surface were presented by Matsumura et al. [11]. These equations can be adapted for other end mill geometries as well.
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F y Analytical
F x Analytical
F y Measured
F x Measured
F z Analytical F z Measured
Fig. 5. Machining forces resolved in the (a) x-, (b) y- and (c) z-axes from both simulations (black dashed line) and measurements (blue, red, and green solid lines, respectively) for inclined flat end milling of the Al6061 workpiece.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The position of a point on the cutting edges can be described in a local x'–y'–z' coordinate system aligned with the cutter axis: 0
x ¼ R cos ðϕÞ
ð5Þ
y0 ¼ R sin ðϕÞ
ð6Þ
z0 ¼ ðR z0 ðkÞÞ
ð7Þ
where ϕ is the immersion angle, which is a function of time and rotational speed, ω (rad/s). The end mill is comprised of k infinitesimal disks along the axial length starting from the bottom of the cutter, each with width dz', so that the axial position along the end mill is z0 ðkÞ ¼ kdz0 The origin of the local cutter coordinates distance R from the bottom to the top of the time t, this point can thus be transformed coordinates by relating to the cutting depth,
ð8Þ is assumed to be end mill. At given into global x–y–z inclination of the
tool, and feed rate 0qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 R2 þ αðγ Þ2 d 0 X ¼ R cos ðϕÞ cos ðγ Þ þ @ R þ z ðkÞA sin ðγ Þ þ f t cos ðθÞ cos ðγ Þ ð9Þ Y ¼ R sin ðϕÞ þ f t sin θ 0qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 R2 þ αðγ Þ2 d 0 @ R þ z ðkÞA cos ðγ Þ Z ¼ R cos ðϕÞ sin ðγ Þ þ cos ðγ Þ
ð10Þ
ð11Þ
where α(γ) is the distance shown in Fig. 2(c) and is dependent on the inclination angle.
αγ ¼
R tan γ
ð12Þ
By iterating through time and the axial position of the cutter, the global coordinates of all points along the cutting edge can be calculated.
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Fig. 7. Average friction coefficient versus normal load measured for flat and dimpled surface under lubricated and unlubricated sliding conditions. All cases were performed for 100 iterations at a speed of 4 mm/s. The friction coefficient reported here represents the average steady-state value of the friction coefficient from approximately cycle 25 to cycle 90 The maximum pressure beneath the sliding ruby sphere calculated using Hertzian contact mechanics for the applied loads measured ranges between 112–175 MPa [27]. The elastic module for aluminum 6061 and Poisson's ratio is 68.9 GPa and 0.33, respectively [28], while the elastic modules and Poisson's ratio for ruby is 3.52 GPa and 0.28 [29], respectively. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 6. (a) Three-dimensional topographic image of the dimpled surfaces produced on the AL6061 workpiece. A blue arrow in (a) marks the sliding direction in relation to the dimple structure used in the friction experiments discussed in the following sections. The white dashed line indicates the place where the line profile shown in (b) was taken. The dimple geometry was produced at a tool incline of 601, a feed rate of 5.0 mm/s, and a spindle speed of 500 rpm.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2.3. Friction measurements Reciprocating friction measurements were conducted under both dry and lubricated conditions (5W30 engine oil) to investigate the effect of the anisotropic profiles of the micro-dimples on the measured friction coefficient. Multiple friction tests were performed in forward and backward sliding directions to study the effect of asymmetrical dimple profiles. The sliding speed of 4 mm/s during friction tests was approximately the fastest sliding speed achievable with the used tribometer. As shown in Fig. 3, friction measurements were performed by removing the end mill bit used for patterning the surface and replacing it with one capped with a ruby half-sphere with a diameter of 6 mm. Reciprocating friction tests were then performed by pressing the ruby-capped end mill against the dimpled surface and then moving the workpiece-table dynamometer assembly horizontally, while measuring the friction and normal forces experienced by the surface with the table dynamometer. The reported values of friction were determined using the following procedure: the normal force (FN) and lateral forces (FL) were the recorded forces in the z- and x-directions and were recorded in both the forward (þx) and backwards ( x) sliding
directions. The average normal force during one reciprocating movement was recorded from the middle 60% of the data points acquired in that reciprocation, and the error represented the standard deviation in that value. Inclusion of this subset of the calculated friction coefficients is intended to remove the turning effects that occur at the start/stop of each reciprocation. The friction force was half of the difference in the lateral force measured at each point along the surface. This calculation was necessary to remove the offset in the lateral force that may have resulted from surface topography [17]. The average friction force was the average value of the friction force for one reciprocation movement; thus, the error in this value was the standard deviation. Fig. 4 shows the average friction coefficient (or the division of the average friction force by the average normal force) as a function of cycle number. Fig. 4 shows the classic wear-in behavior often seen in tribological experiments, where the friction coefficient drastically decreases in the initial sliding cycles and then reaches a plateau or steady-state value at higher cycle numbers. The average friction coefficient is determined from only those cycle numbers where the steady-state friction coefficient has been achieved. The surface topography was measured with white light interferometry (Zygo Zescope).
3. Results 3.1. Forces exhibited by flat end mill during machining Force modeling of machining operations is central to understanding how to improve longevity and efficiency, so that accurate modeling of cutting forces is important in order to generate desired surface patterns without causing tool breakage and excessive tool deflection [18]. In addition, the predicted forces are essential for determining the optimal process parameters for forming high-quality components.
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Fig. 8. Friction coefficient measured during reciprocating motion of the tribometer applying a normal force of 18.5 N for (a) lubricated flat surface in forward and backward direction, friction coefficient of 0.1417 0.010 for both forward and backward directions, and (b) lubricated dimpled surface in forward and backward directions with friction coefficient of 0.1267 0.009 for the forward directions and 0.1317 0.009 for the backward direction.
Fig. 5 shows the simulated machining forces, as well as the forces measured by the table dynamometer resolved into forces, measured in the x-, y-, and z-directions. The comparison between the simulation and experimental results relied on the following condition: dimples were machined into the surface when the cutting edge was engaged onto the workpiece surface, which occurred when the z coordinate of a point on the cutting edges was less than zero (z o0). Simulated machining forces also used Eqs. (9)–(11) to achieve analytical profiles of dimple patterns, also revealing the resulting dimple shape and size. Fig. 5 shows the validity of the analytical model describing the machining forces and also shows that the peak forces measured in alternating cuts was slightly higher than in the cut directly beforehand. This observation suggests that the flat end mill was not completely symmetric. The influence of this variation in cutting forces is described in Section 3.2. Measured forces present some discrepancies with respect to analytical forces. In this study, it can be especially observed in the y direction force. Factors as additional frictional forces on the flank face of the cutting edges due to elastic recovery of material, geometric non-uniformity in the cutting tool, cutter run-out, and eccentricity may cause less material to be removed in this direction compared with the x and y direction forces, also affecting the depth between successive dimples and contributing to the difference between measured and analytical forces [10,18]. It is also important to mention that the cutting and edge coefficients need to be identified for different machining setups, tools, and workpieces: mechanistic models can be highly accurate [16].
3.2. Profile of dimpled Surfaces produced with flat end mill Fig. 6(a) shows the measured topographic profile of the dimpled surfaces produced at a constant inclination angle of 601. A close examination of Fig. 6(b) shows that the dimpled patterns had a depth of approximately 30 mm with the aforementioned machining parameters, which was significantly higher than the average surface roughness. The size of the dimples in comparison to the surface roughness was also evident by the flatness of the surface surrounding the dimples in these topographic images. The influence of the asymmetically shaped end mill that produced the force variations in Fig. 5 can also be seen in Fig. 6. When observing the dimples from left to right in Fig. 6, the lateral dimensions on every second dimple, had slightly smaller plane
view dimensions, as shown in Fig. 6(a), and a slightly smaller depth (by approximately 5 mm), as shown in Fig. 6(b). 3.3. Friction results In mechanical systems, friction is the primary cause of energy loss. By patterning the surface with micro-dimples, a reduction in the sliding friction can be achieved, because the dimple geometry and distribution affects the development of hydrodynamic pressure between sliding surfaces in lubricated mechanical systems [7]. Greater energy efficiency, reduced emissions and lessened environmental impact are potential benefits that result from the use of patterned surfaces to reduce friction in mechanical systems. Using the inclined micro-milling technique with a flat end mill, we investigated a further application of patterned surfaces: anisotropic or sliding direction dependent friction coefficients resulting from the variation in hydrodynamic pressures that occur when sliding from left to right versus right to left. Friction tests were performed to study the performance of unique surfaces patterns obtained by using the inclined micro-milling technique and flat end mills. Fig. 7 shows the average friction coefficient versus the applied normal force. The sliding direction in relation to the dimple structure is shown in Fig. 6(a). As expected, Fig. 7 shows a lower friction coefficient for both the lubricated flat (hollow black squares) and dimpled (hollow red circles) surfaces, compared to unlubricated flat (filled black squares) and dimpled (filled red circles) surfaces. In both lubricated and unlubricated conditions, the dimpled surfaces produced lower coefficients than those of the flat surfaces. The observed lower friction coefficients of friction on dimpled surfaces in comparison to flat surfaces were consistent with previous studies of lubrication [5,19–24]. Fig. 8 shows the lateral force divided by the average normal force for two reciprocating motions of the tribometer under lubricated conditions for flat and dimpled surfaces. The lateral force offset from the topography was determined on the flat surface and applied to both data sets. Determination of the offset for the zero value of force offset from the untextured surface assumes the friction loop has the same value as the forward and reverse sliding directions. Given the analysis of the friction data presented in similar studies of friction on textured surface, a similar assumptions regarding the symmetry of the friction loops has been made for these surfaces [25,26]. As expected, the friction coefficient on the lubricated dimpled surface in Fig. 8(b), on average, was lower than that for the lubricated flat
J. Resendiz et al. / Tribology International 91 (2015) 67–73
surface in Fig. 8(a). The average friction coefficients for the forward and reverse sliding directions were calculated from the data shown in Fig. 8, neglecting the first and last 20% of the data points to remove turning effects. Both the forward and reverse friction coefficients on the flat lubricated surface were 0.1417 0.010, while on the dimpled surface, a friction coefficient of 0.126 70.009 was measured in the forward direction and 0.131 70.009 in the reverse direction. It is proposed that the hydrodynamic pressure when sliding over these asymmetrically shaped dimples depends on the sliding direction. Further experimentation, as well as corresponding simulation of the hydrodynamic pressures between the surfaces, is required to verify this hypothesis. 4. Conclusion Dimpled surfaces with an asymmetric geometry have been produced with a flat end mill in an aluminum workpiece. Modeling of the forces and the dimple geometry allows for predictive determination of the size, shape, distribution and end mill requirements for patterning surfaces. These calculations were validated by comparing the measured forces during milling the dimpled surfaces with the calculated forces from our machining model. The comparison between the model and experimental measurements of the machining forces also allowed for the determination of tool asymmetry, which could be correlated with variations in the geometry of the machined dimple pattern. The comparison of dimpled and flat surfaces show that, under both lubricated and unlubricated sliding conditions, dimpled surfaces resulted in lower measured friction coefficients, which is consistent with the literature on symmetrically shaped dimples [4–7]. Furthermore, asymmetrically shaped dimples have been shown to have a sliding direction dependent response, in terms of the measured friction forces and friction coefficient, in comparison with flat surfaces. Acknowledgments We would like to acknowledge Transportation Canada for Railing Research, the National Council of Science and Technology (CONACYT) of Mexico and the Natural Sciences and Engineering Research Council (NSERC) of Canada for providing funds to support the study. References [1] Bruzzone AAG, Costa HL, Lonardo PM, Lucca DA. Advances in engineered surfaces for functional performance. CIRP Ann: Manuf Technol 2008;57:750–69. http://dx.doi.org/10.1016/j.cirp.2008.09.003. [2] Rabinowicz E. Friction and Wear of Materials. 2nd ed.. New York: Wiley; 2013. p. 336 (Chapter 4). [3] Ito H, Kaneda K, Yuhta T, Nishimura I, Yasuda K, Matsuno T. Reduction of polyethylene wear by concave dimples on the frictional surface in artificial hip joints. J Arthroplast 2000;15:332–8. http://dx.doi.org/10.1016/S0883-5403(00) 90670-3. [4] Denkena B, Kästner J, Wang B. Advanced microstructures and its production through cutting and grinding. CIRP Ann:Manuf Technol 2010;59:67–72. http: //dx.doi.org/10.1016/j.cirp.2010.03.066.
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Directional friction surfaces through asymmetrically shaped dimpled surfaces patterned using inclined flat end milling Jesus Resendiz, Eldon Graham, Philip Egberts n, Simon S. Park Micro Engineering Dynamics and Automation Laboratory (MEDAL), Department of Mechanical & Manufacturing Engineering, University of Calgary, 40 Research Place NW, Calgary, Alberta, Canada T2L 1Y6
art ic l e i nf o
a b s t r a c t
Article history: Received 4 March 2015 Received in revised form 28 May 2015 Accepted 19 June 2015 Available online 29 June 2015
In this study, directional friction effects by creating asymmetrically shaped dimpled surfaces on an aluminum workpiece were investigated. The surfaces were created using the inclined micro-flat end milling process. Inclined micro-milling forces were modeled, and subsequent comparisons with the measured forces have provided validation. These simulations also showed that the flat end mill used to produce these dimpled surfaces was not symmetric. Tribological characterization of the friction properties of the surface using reciprocating tribometer and a hemispherical ruby counter surface indicated that these asymmetrically shaped dimples lowered the overall friction coefficients measured under both dry and lubricated sliding conditions. Moreover, the results also demonstrated a sliding direction dependent response, in terms of the measured friction coefficients. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Micro-patterns Functional surfaces Micro-flat end milling Friction
1. Introduction Functional surfaces play an important role in the behavior of engineering parts, such as those in mechanics, electronics, information technology, energy, optics, biology, and biomimetics [1]. Reduction of friction depends on many factors: one of the important factors is the topography of the rubbing interfaces [2]. For example, patterned surfaces are one mechanism by which the lifetime of hip replacements can be extended [3]. In more conventional engineering mechanical systems, such as in automotive lubrication, functional surfaces in the form of microdimples have been shown to reduce friction between mechanical components through the following mechanisms: debris caused by mechanical wear of the sliding surfaces can be trapped by the textured surface [1,4]; the textured patterns can act as lubricant reservoirs, allowing for a faster transition to the elastohydrodynamic lubrication regime as the device is switched on [5]; and, textured surfaces can also influence the hydrodynamic pressure between surfaces, which can result in increased load carrying capacity [4,6,7]. Since uniformly shaped surface features can be difficult to produce, many researchers have observed anisotropic frictional effects that depend upon the orientation of surface features to the n
Corresponding author at: 40 Research Place NW, Calgary AB, T2L 1Y6. E-mail addresses: [email protected] (J. Resendiz), [email protected] (E. Graham), [email protected] (P. Egberts), [email protected] (S.S. Park). http://dx.doi.org/10.1016/j.triboint.2015.06.025 0301-679X/& 2015 Elsevier Ltd. All rights reserved.
sliding direction [8]. Depending upon the type of surface structures, frictional performance is often superior in a specific direction [4,9]. In fact, anisotropic frictional effects arise naturally in many materials, such as wood and composites, due to the material structure and surface roughness [8]. Compared to other surface texturing methods, such as wet or dry etchings, abrasive jet machining and laser processes, inclined micro-milling can be an efficient and cost-effective method to fabricate micro-dimples, because complex systems are not necessary. Inclined micro-milling is very precise and does not have high energy consumption, and a mask is not required. The micromilling technique significantly reduces the time needed to fabricate dimpled surfaces by creating a row of dimples in a single pass of the cutter. Many other machining methods are not efficient by comparison, as individual dimples are made through repeated horizontal and vertical movements of the cutting tool; thus, pattern surfaces from inclined micro-milling exhibit improved tribological properties [10]. Determination of the optimal structure that can influence the friction response of a mechanical system is of particular interest. Such surfaces have been realized through ball end milling [11] and fly cutting [12]. Advantages of micro-milling producing microtextured surfaces include high material removal rates, accurate surface finishes, and few restrictions on workpiece materials [13]. It has also been shown that micro-milling can be used to produce a variety of different surface structures by altering the cutting technique [14]. Micro-milling thus represents a very flexible method, and, with the right combination of cutting technique
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and tool geometry, a wide variety of surface structures can be developed. However, care must be taken when using micromilling to pattern surfaces, as in machining patterns, oscillations of cutters while rotating, cutting tool wear or breakage, tool deflections, non-uniformity of cutting conditions, varying rigidity of the workpiece or clamping system, and abrupt movements of the workpiece while texturing can detrimentally influence the resulting surface structure [15]. Predictive modeling of the machining forces is one mechanism by which of these disadvantages can be reduced, as several of these challenges can be identified beforehand, such as cutting tool wear or breakage and tool deflections. Furthermore, comparison of measured machining forces with those predicted by the model can be used to identify issues with patterning the surface, such as issues with uniform cutting, oscillations in the cutter, or tool wear. The performance of textured surfaces depends upon the geometry of the surface patterns. It is, therefore, essential to understand how different machining parameters affect the resulting topographic structure. In this paper, the cutting forces are evaluated to determine the effect of machining parameters on tool longevity and efficiency, as well as patterning performance and efficiency. The surface topography generated by a flat end mill on aluminum alloy Al6061 is characterized to ensure the machining simulations match experimental measurements. Finally, the tribological performance of anisotropically shaped micro-dimples is evaluated and shown to have sliding direction dependent friction coefficients. An understanding of the basic relationship between these parameters allows manufacturers to optimize the tool path and surface features and minimize, tool wear and deflection.
2. Methods
the stage using a Keyence Laser Displacement Sensor (LK-G3001) in relation to the number of steps counted during the translation of the stage. Samples were produced by fixing the Al6061 workpiece to a piezoelectric table dynamometer (Kistler 9256C), allowing for future measurements of cutting and friction forces. Before producing dimples, the surface of the aluminum workpiece was flattened by milling the top layer of the surface with the spindle positioned so that its long axis was perpendicular to the workpiece surface normal. To ensure a sufficient supply of oil for lubricated surfaces during friction testing, a small depression of about 2 mm was machined onto the surface of half of the workpiece. This depression ensured that the lubricated and unlubricated surfaces had the exact same surface normal in subsequent friction testing. Following the surface planning and milling of the oil reservoir, the surfaces were polished using a P800 grit sandpaper to remove machining marks and reduce surface roughness. The surface roughness was measured over a 1 1 mm2 area to be less than 0.11 70.02 mm (Mitutoyo SJ-201P). To measure cutting during dimple fabrication and friction forces, analog signals from the table dynamometer were amplified by a factor of 10 (Kistler Charge Amplifier 5010) and digitally recorded (National Instruments BNC-2110) at a sampling rate of 1 kHz. Dimpled surfaces were produced by fast translation of the sample workpiece while the end mill, now inclined at angle of 601 to the surface normal, was close enough for the flutes to cut the surface. A flat end mill (PMTs TS-2-0350-S) containing two flutes and with a diameter of 889.0 μm was used, producing dimples of approximately asymmetrically shaped dimples that were approximately 30 mm deep and 300 mm in the largest lateral dimension. Further details of the shape of the resulting surface texture are discussed in the next section.
2.1. Machining of patterned surfaces Flat and dimpled surfaces were machined using a home-built computer numerical control (CNC) micro-milling system. This system is graphically depicted in Fig. 1(a) and photographed in Fig. 1(b). The CNC was mounted and secured on a vibration isolation table to insulate the machining system from the ground. An electric spindle (NSK Astro-E 800Z) was mounted onto a bracket that allowed the spindle to rotate at an inclination angle relative to the sample surface and to be secured during machining. Translation of the workpiece below the spindle during machining and friction testing was achieved by mounting the workpiece on linear precision stages (Parker Daedal 10600). These linear precision stages were actuated with stepper motors that were computer controlled (National Instruments PXI-1042Q). Calibration of the stepper motors was made by measuring the real displacement of
2.2. Modeling of inclined flat end milling forces Conventional cutting force models for flat end mills can be modified to predict forces for inclined flat end milling. Three force components on the milling cutter must be considered to account for the effects of spindle inclination. Inclined cutting of dimples with a flat end mill is periodic and not continuous as in upright milling, and each flute enters the workpiece surface with a certain frequency. Since the tool geometry of a flat end mill allows for uniquely shaped dimple geometries, an investigation into how cutting forces are affected is warranted. Using the conventional force model, cutting forces can be identified while the end mill is inclined in local x'–y'–z' coordinates. Afterwards, they can be
Fig. 1. (a) Schematic of the machining system used. The flat end mill is tilted with respect to the surface normal of the workpiece to produce the dimpled surface. (b) Photograph of the end mill setup used to produce the dimpled surfaces. The spindle in this case is at an inclination angle (γ) of 601 with a flat end mill attached.
J. Resendiz et al. / Tribology International 91 (2015) 67–73
z’
z R
ϒ
z’
f Aluminum Workpiece
R
φ
R
x’
x’
θ=0
x
y’
y’ φ
y
n
ϒ
n
z’ ϒ
69
f
x’
α (ϒ)
z’(k) R
d
d
Fig. 2. Analytic model of a flat end mill. (a) The tool is inclined at angle γ and helix angle β. When the tool moves through the workpiece surface, each flute successively cuts a dimple into the material at cutting depth d. (b) A cylindrical micro-end mill can be modeled as rotating element with spindle speed n (rev/min) that moves with feed rate f (mm/s), and the position of a point on the cutting edges can be described in x'–y'–z' coordinates. (c) Knowing a point with distance R from the bottom of the end mill and the top of the end mill at given time t, it is possible to transform this point to global x–y–z coordinates by relating to the cutting depth, inclination of the tool, and feed rate.
Capped End Mill with a Ruby Half-Sphere
Aluminum 6061 workpiece
Wear Groove Caused by Friction Reciprocation
Laser Displacement Sensor
Spindle at 0° Inclination
Table Dynamometer
Fig. 3. Photograph of friction measurement apparatus/tribometer. A 6 mm ruby ball is attached at the end of an end mill held stationary, while the workpiece, attached to a table dynamometer (a 3-axis force sensor), is moved in a reciprocating motion. A laser displacement sensor measures the stage movement.
transformed back through the inclination angle to the global x–y–z coordinate system. The conventional mechanistic force model for shearing dominant cutting for a flat end mill determines forces by calculating the chip thickness and identifying cutting coefficients [16]. The conventional force model for standard upright helical end mills describes three force components (tangential, radial, and axial). The general formula for the chip thickness h of a flat end mill is given by h ¼ f t sin ðϕÞ
ð1Þ
where ft is the feed rate (mm/flute), and ϕ is the tool rotation angle adjusted for the number of flutes and position along the cutting edge. End mills experience a resultant force comprised of three components in the radial, Fr, tangential, Ft, and axial, Fa, directions. For shearing dominant cutting [16], the elemental component of each can be expressed as: dF r ¼ K rc hdz0 þ K re dz0
ð2Þ
dF t ¼ K tc hdz0 þK te dz0
ð3Þ
dF a ¼ K ac hdz0 þ K ae dz0
ð4Þ
where Krc, Ktc, Kac, Kre, Kte and Kae are the cutting and edge coefficients in each direction, respectively, and dz' is the differential axial height of the cutter.
Fig. 4. Measured friction coefficient versus cycle number for a flat, oil-lubricated surface. One hundred reciprocation cycles were recorded at an applied load of 5 N on the Al6061 workpiece. The green square shows the region from which the steady-state friction coefficient was determined, which approximately corresponds to friction coefficients recorded from cycle numbers 25–90.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The cutting coefficients depend on the tool geometry and workpiece material and are different for each cutting tool and workpiece combination. These parameters must be identified experimentally from cutting tests. Surface topography can be predicted analytically by relating tool geometry and machining parameters to the workpiece surface. As shown in Fig. 2, a cylindrical micro-end mill can be modeled as rotating with spindle speed n (rev/min) and moved at feed rate f (mm/s). The tool is inclined at angle γ and has radius R, N number of flutes, and helix angle β. As the tool moves over the workpiece surface, each flute successively cuts a dimple into the material at maximum cutting depth d. The angular direction of feed θ is defined from the x-axis. For this study, the spindle was inclined about the y-axis in the same direction as the tool feed or x-direction (θ ¼ 0). The equations that relate an inclined ball end mill with the position of the cutting edge to a flat workpiece surface were presented by Matsumura et al. [11]. These equations can be adapted for other end mill geometries as well.
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F y Analytical
F x Analytical
F y Measured
F x Measured
F z Analytical F z Measured
Fig. 5. Machining forces resolved in the (a) x-, (b) y- and (c) z-axes from both simulations (black dashed line) and measurements (blue, red, and green solid lines, respectively) for inclined flat end milling of the Al6061 workpiece.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The position of a point on the cutting edges can be described in a local x'–y'–z' coordinate system aligned with the cutter axis: 0
x ¼ R cos ðϕÞ
ð5Þ
y0 ¼ R sin ðϕÞ
ð6Þ
z0 ¼ ðR z0 ðkÞÞ
ð7Þ
where ϕ is the immersion angle, which is a function of time and rotational speed, ω (rad/s). The end mill is comprised of k infinitesimal disks along the axial length starting from the bottom of the cutter, each with width dz', so that the axial position along the end mill is z0 ðkÞ ¼ kdz0 The origin of the local cutter coordinates distance R from the bottom to the top of the time t, this point can thus be transformed coordinates by relating to the cutting depth,
ð8Þ is assumed to be end mill. At given into global x–y–z inclination of the
tool, and feed rate 0qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 R2 þ αðγ Þ2 d 0 X ¼ R cos ðϕÞ cos ðγ Þ þ @ R þ z ðkÞA sin ðγ Þ þ f t cos ðθÞ cos ðγ Þ ð9Þ Y ¼ R sin ðϕÞ þ f t sin θ 0qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 R2 þ αðγ Þ2 d 0 @ R þ z ðkÞA cos ðγ Þ Z ¼ R cos ðϕÞ sin ðγ Þ þ cos ðγ Þ
ð10Þ
ð11Þ
where α(γ) is the distance shown in Fig. 2(c) and is dependent on the inclination angle.
αγ ¼
R tan γ
ð12Þ
By iterating through time and the axial position of the cutter, the global coordinates of all points along the cutting edge can be calculated.
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Fig. 7. Average friction coefficient versus normal load measured for flat and dimpled surface under lubricated and unlubricated sliding conditions. All cases were performed for 100 iterations at a speed of 4 mm/s. The friction coefficient reported here represents the average steady-state value of the friction coefficient from approximately cycle 25 to cycle 90 The maximum pressure beneath the sliding ruby sphere calculated using Hertzian contact mechanics for the applied loads measured ranges between 112–175 MPa [27]. The elastic module for aluminum 6061 and Poisson's ratio is 68.9 GPa and 0.33, respectively [28], while the elastic modules and Poisson's ratio for ruby is 3.52 GPa and 0.28 [29], respectively. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 6. (a) Three-dimensional topographic image of the dimpled surfaces produced on the AL6061 workpiece. A blue arrow in (a) marks the sliding direction in relation to the dimple structure used in the friction experiments discussed in the following sections. The white dashed line indicates the place where the line profile shown in (b) was taken. The dimple geometry was produced at a tool incline of 601, a feed rate of 5.0 mm/s, and a spindle speed of 500 rpm.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2.3. Friction measurements Reciprocating friction measurements were conducted under both dry and lubricated conditions (5W30 engine oil) to investigate the effect of the anisotropic profiles of the micro-dimples on the measured friction coefficient. Multiple friction tests were performed in forward and backward sliding directions to study the effect of asymmetrical dimple profiles. The sliding speed of 4 mm/s during friction tests was approximately the fastest sliding speed achievable with the used tribometer. As shown in Fig. 3, friction measurements were performed by removing the end mill bit used for patterning the surface and replacing it with one capped with a ruby half-sphere with a diameter of 6 mm. Reciprocating friction tests were then performed by pressing the ruby-capped end mill against the dimpled surface and then moving the workpiece-table dynamometer assembly horizontally, while measuring the friction and normal forces experienced by the surface with the table dynamometer. The reported values of friction were determined using the following procedure: the normal force (FN) and lateral forces (FL) were the recorded forces in the z- and x-directions and were recorded in both the forward (þx) and backwards ( x) sliding
directions. The average normal force during one reciprocating movement was recorded from the middle 60% of the data points acquired in that reciprocation, and the error represented the standard deviation in that value. Inclusion of this subset of the calculated friction coefficients is intended to remove the turning effects that occur at the start/stop of each reciprocation. The friction force was half of the difference in the lateral force measured at each point along the surface. This calculation was necessary to remove the offset in the lateral force that may have resulted from surface topography [17]. The average friction force was the average value of the friction force for one reciprocation movement; thus, the error in this value was the standard deviation. Fig. 4 shows the average friction coefficient (or the division of the average friction force by the average normal force) as a function of cycle number. Fig. 4 shows the classic wear-in behavior often seen in tribological experiments, where the friction coefficient drastically decreases in the initial sliding cycles and then reaches a plateau or steady-state value at higher cycle numbers. The average friction coefficient is determined from only those cycle numbers where the steady-state friction coefficient has been achieved. The surface topography was measured with white light interferometry (Zygo Zescope).
3. Results 3.1. Forces exhibited by flat end mill during machining Force modeling of machining operations is central to understanding how to improve longevity and efficiency, so that accurate modeling of cutting forces is important in order to generate desired surface patterns without causing tool breakage and excessive tool deflection [18]. In addition, the predicted forces are essential for determining the optimal process parameters for forming high-quality components.
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Fig. 8. Friction coefficient measured during reciprocating motion of the tribometer applying a normal force of 18.5 N for (a) lubricated flat surface in forward and backward direction, friction coefficient of 0.1417 0.010 for both forward and backward directions, and (b) lubricated dimpled surface in forward and backward directions with friction coefficient of 0.1267 0.009 for the forward directions and 0.1317 0.009 for the backward direction.
Fig. 5 shows the simulated machining forces, as well as the forces measured by the table dynamometer resolved into forces, measured in the x-, y-, and z-directions. The comparison between the simulation and experimental results relied on the following condition: dimples were machined into the surface when the cutting edge was engaged onto the workpiece surface, which occurred when the z coordinate of a point on the cutting edges was less than zero (z o0). Simulated machining forces also used Eqs. (9)–(11) to achieve analytical profiles of dimple patterns, also revealing the resulting dimple shape and size. Fig. 5 shows the validity of the analytical model describing the machining forces and also shows that the peak forces measured in alternating cuts was slightly higher than in the cut directly beforehand. This observation suggests that the flat end mill was not completely symmetric. The influence of this variation in cutting forces is described in Section 3.2. Measured forces present some discrepancies with respect to analytical forces. In this study, it can be especially observed in the y direction force. Factors as additional frictional forces on the flank face of the cutting edges due to elastic recovery of material, geometric non-uniformity in the cutting tool, cutter run-out, and eccentricity may cause less material to be removed in this direction compared with the x and y direction forces, also affecting the depth between successive dimples and contributing to the difference between measured and analytical forces [10,18]. It is also important to mention that the cutting and edge coefficients need to be identified for different machining setups, tools, and workpieces: mechanistic models can be highly accurate [16].
3.2. Profile of dimpled Surfaces produced with flat end mill Fig. 6(a) shows the measured topographic profile of the dimpled surfaces produced at a constant inclination angle of 601. A close examination of Fig. 6(b) shows that the dimpled patterns had a depth of approximately 30 mm with the aforementioned machining parameters, which was significantly higher than the average surface roughness. The size of the dimples in comparison to the surface roughness was also evident by the flatness of the surface surrounding the dimples in these topographic images. The influence of the asymmetically shaped end mill that produced the force variations in Fig. 5 can also be seen in Fig. 6. When observing the dimples from left to right in Fig. 6, the lateral dimensions on every second dimple, had slightly smaller plane
view dimensions, as shown in Fig. 6(a), and a slightly smaller depth (by approximately 5 mm), as shown in Fig. 6(b). 3.3. Friction results In mechanical systems, friction is the primary cause of energy loss. By patterning the surface with micro-dimples, a reduction in the sliding friction can be achieved, because the dimple geometry and distribution affects the development of hydrodynamic pressure between sliding surfaces in lubricated mechanical systems [7]. Greater energy efficiency, reduced emissions and lessened environmental impact are potential benefits that result from the use of patterned surfaces to reduce friction in mechanical systems. Using the inclined micro-milling technique with a flat end mill, we investigated a further application of patterned surfaces: anisotropic or sliding direction dependent friction coefficients resulting from the variation in hydrodynamic pressures that occur when sliding from left to right versus right to left. Friction tests were performed to study the performance of unique surfaces patterns obtained by using the inclined micro-milling technique and flat end mills. Fig. 7 shows the average friction coefficient versus the applied normal force. The sliding direction in relation to the dimple structure is shown in Fig. 6(a). As expected, Fig. 7 shows a lower friction coefficient for both the lubricated flat (hollow black squares) and dimpled (hollow red circles) surfaces, compared to unlubricated flat (filled black squares) and dimpled (filled red circles) surfaces. In both lubricated and unlubricated conditions, the dimpled surfaces produced lower coefficients than those of the flat surfaces. The observed lower friction coefficients of friction on dimpled surfaces in comparison to flat surfaces were consistent with previous studies of lubrication [5,19–24]. Fig. 8 shows the lateral force divided by the average normal force for two reciprocating motions of the tribometer under lubricated conditions for flat and dimpled surfaces. The lateral force offset from the topography was determined on the flat surface and applied to both data sets. Determination of the offset for the zero value of force offset from the untextured surface assumes the friction loop has the same value as the forward and reverse sliding directions. Given the analysis of the friction data presented in similar studies of friction on textured surface, a similar assumptions regarding the symmetry of the friction loops has been made for these surfaces [25,26]. As expected, the friction coefficient on the lubricated dimpled surface in Fig. 8(b), on average, was lower than that for the lubricated flat
J. Resendiz et al. / Tribology International 91 (2015) 67–73
surface in Fig. 8(a). The average friction coefficients for the forward and reverse sliding directions were calculated from the data shown in Fig. 8, neglecting the first and last 20% of the data points to remove turning effects. Both the forward and reverse friction coefficients on the flat lubricated surface were 0.1417 0.010, while on the dimpled surface, a friction coefficient of 0.126 70.009 was measured in the forward direction and 0.131 70.009 in the reverse direction. It is proposed that the hydrodynamic pressure when sliding over these asymmetrically shaped dimples depends on the sliding direction. Further experimentation, as well as corresponding simulation of the hydrodynamic pressures between the surfaces, is required to verify this hypothesis. 4. Conclusion Dimpled surfaces with an asymmetric geometry have been produced with a flat end mill in an aluminum workpiece. Modeling of the forces and the dimple geometry allows for predictive determination of the size, shape, distribution and end mill requirements for patterning surfaces. These calculations were validated by comparing the measured forces during milling the dimpled surfaces with the calculated forces from our machining model. The comparison between the model and experimental measurements of the machining forces also allowed for the determination of tool asymmetry, which could be correlated with variations in the geometry of the machined dimple pattern. The comparison of dimpled and flat surfaces show that, under both lubricated and unlubricated sliding conditions, dimpled surfaces resulted in lower measured friction coefficients, which is consistent with the literature on symmetrically shaped dimples [4–7]. Furthermore, asymmetrically shaped dimples have been shown to have a sliding direction dependent response, in terms of the measured friction forces and friction coefficient, in comparison with flat surfaces. Acknowledgments We would like to acknowledge Transportation Canada for Railing Research, the National Council of Science and Technology (CONACYT) of Mexico and the Natural Sciences and Engineering Research Council (NSERC) of Canada for providing funds to support the study. References [1] Bruzzone AAG, Costa HL, Lonardo PM, Lucca DA. Advances in engineered surfaces for functional performance. CIRP Ann: Manuf Technol 2008;57:750–69. http://dx.doi.org/10.1016/j.cirp.2008.09.003. [2] Rabinowicz E. Friction and Wear of Materials. 2nd ed.. New York: Wiley; 2013. p. 336 (Chapter 4). [3] Ito H, Kaneda K, Yuhta T, Nishimura I, Yasuda K, Matsuno T. Reduction of polyethylene wear by concave dimples on the frictional surface in artificial hip joints. J Arthroplast 2000;15:332–8. http://dx.doi.org/10.1016/S0883-5403(00) 90670-3. [4] Denkena B, Kästner J, Wang B. Advanced microstructures and its production through cutting and grinding. CIRP Ann:Manuf Technol 2010;59:67–72. http: //dx.doi.org/10.1016/j.cirp.2010.03.066.
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