Wear characteristics of large aspect ratio silicon microbearing systems

Wear 312 (2014) 58–69

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Wear characteristics of large aspect ratio silicon microbearing systems S. Demiri a, S. Boedo b,n, L.S. Holsen b a b

Microsystems Engineering, Rochester Institute of Technology, Rochester, NY 14623, United States Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY 14623, United States

art ic l e i nf o

a b s t r a c t

Article history: Received 11 November 2013 Received in revised form 25 January 2014 Accepted 31 January 2014 Available online 11 February 2014

This paper addresses the wear characteristics of large aspect ratio (length-to-diameter) silicon microbearing systems using an enhanced experimental test rig. The test system is comprised of a rigid rotor which has been manually assembled onto a fixed hub to form the microbearing. CMOS-based lithographic and etching processes, including deep-reactive ion etching, are employed in the construction of the rotor and hub with length to diameter ratio of approximately 0.5 and radial clearance values in the range from 3.5 to 9.2 μm. The rotor is pneumatically driven by nitrogen gas at a constant supply pressure delivered through a rectangular microchannel. A new methodology for measuring wear was developed by digitizing optical microscope images of the rotor system, and the rotor load was calculated from CFD models of the entire rotor-hub system. It was found that the tested silicon microbearings have a wear coefficient (based on the well-known Archard relation) which falls within a relatively narrow band bounded by previously published values for polysilicon materials tested at the macroscale and microscale. The wear coefficient is also observed to be relatively unchanged during the wear process which is more characteristic of macroscale wear processes. & 2014 Elsevier B.V. All rights reserved.

Keywords: MEMS Microsystems Tribology Journal bearings Wear

1. Introduction Advancements in integrated-circuit (IC) processing have led to the introduction of silicon-based microelectromechanical systems (MEMS). Silicon's prominence within MEMS is attributed to its strength, electrical, and oxidation characteristics [1]. The range of MEMS applications has been rapidly expanding in response to increasing demands for mobility and multifunctionality at low cost. A key incentive fueling the development of microsystems such as microturbines, micropumps, microgears, and lab-on-chip systems is the low unit cost resulting from mass-fabrication of complex, integrated, silicon-based microsystems by borrowing from many established precision IC processing techniques. In the quest for commercialization, the primary inhibitor to date has been bearing reliability. This is particularly true for high speed operation (on the order of tens of thousands to millions of revolutions per minute) where seizure, high wear rates [2], and complete destruction [3] have been observed. Surprisingly, relatively little is understood about the wear behavior of large aspect ratio microbearings. In the past, researchers have worked primarily on surface micromachined polysilicon

n

Corresponding author. Tel.: þ 1 585 475 5214; fax: þ1 585 475 7710. E-mail addresses: [email protected] (S. Demiri), [email protected] (S. Boedo), [email protected] (L.S. Holsen). http://dx.doi.org/10.1016/j.wear.2014.01.016 0043-1648 & 2014 Elsevier B.V. All rights reserved.

electric-driven rotating machinery. The design space available for employing this fabrication methodology has resulted in bearings with length-to-diameter (L/D) aspect ratios on the order of 0.05. This ultra-low aspect ratio is due to limitations of surface micromachining planar fabrication technology. More recently, wear characteristics of larger aspect ratio (
0.6) plain cylindrical journal bearings fabricated using X-ray lithography, Ni electroplating, and tungsten alloy coatings were reported [4]. Results indicated that coated microbearings had lower wear rates than uncoated bearings. Recently, the authors reported on the first published study which investigated the wear behavior of large-aspect ratio siliconbased microbearings [5]. The experimental system, denoted as Phase 1, is shown in Fig. 1. The system is characterized by a rigid rotor which has been manually assembled onto a fixed hub to form the microbearing. Rotor (out-of-plane) thickness ranges from 150 to 200 μm, and the rotor diameter is approximately 400 μm, resulting in a relatively large length to diameter ratio of 0.38–0.5. The rotor is pneumatically driven by nitrogen gas which enters a drilled access hole from the backside of the hub and flows through one of the rectangular microchannels. It was found that wear progression was substantially dependent on bearing geometry for bearing configurations with similar average clearance values. Observed wear morphology was strongly suggestive of impact damage, as shown in Fig. 2, and could not be attributed to an adhesion or abrasion wear model. Moreover, the

S. Demiri et al. / Wear 312 (2014) 58–69

Nomenclature Aw B C D F H K L Ls N P0 R R1 V W

debris area [L2] hub length [L] radial clearance [L] rotor diameter [L] radial load [F] material hardness [FL  2] wear coefficient [  ] rotor out-of-plane thickness [L] wear path length [L] number of thrust pads [  ] ambient pressure [FL  2] hub nominal radius [L] hub radius, top surface [L] volumetric wear [L3] thrust load [F]

observed impact damage was thought to be associated more with the physical limitations and test protocol of the Phase 1 experimental rig, characterized by large clearance specifications and lack of thrust bearing surfaces, compared with what would be expected in an actual application. This paper provides an assessment of the effects of bearing clearance on the wear behavior of large aspect ratio silicon-based gas microbearings using a new Phase 2 test apparatus. Tighter clearances, constant supply pressure, and the use of gas thrust bearing surfaces are employed in the new design.

2. Material and methods As in Phase 1, rotors and hubs are fabricated on separate silicon wafers and are manually assembled to form the microbearing system. In this manner, radial clearances as small as 1 μm are possible for bearing aspect ratios considered here. Novel “sprue” and “float” etching techniques involving KOH and deep reactive ion etching (DRIE) processes are employed in the fabrication of the hub and rotor, as described in detail elsewhere [5,6]. Phase 2 nominal rotor thickness and diameter specifications are 190 and 400 mm, respectively, resulting in an L/D ratio of 0.48 which is similar to that employed in Phase 1. Fig. 3 shows several new features which are incorporated into the Phase 2 hub design. A single straight microchannel which is shorter than the Phase 1 design reduces the pressure drop from the source to the hub teeth. As discussed below, nitrogen gas is supplied from the top surface of the hub to the microchannel, eliminating the need for wafer dicing and drilling access holes into the brittle silicon. Sectored thrust pads are incorporated into the bottom of the hub base using a separate photolithographic mask pattern. The design intent of the pads is to promote full-film gas lubrication between the bottom of the rotor and the base of the hub, which in turn reduces contract friction, increases rotational speed, and stabilizes out-of-plane rotor motion. Fabricated hubs are shown in Figs. 4 and 5. The hub is now formed as a hollow shaft to assist in the alignment of a fiber optic cable for rotor speed measurements. Figs. 6 and 7 show an exploded view schematic and assembly of the Phase 2 microbearing test fixture. The entire undiced wafer is placed on a precision ground 8 mm thick stainless steel plate. A polycarbonate plate and silicone sheet, each 1 mm thick, and each containing drilled access holes are aligned over the hub wafer. A top steel plate with access holes is bolted to the bottom plate which compresses the silicone sheet and seals the fixture. “Push-

a b e h r1 tw x,y,z

Δ α δ ε θ μ s ψ0 ω

59

pad effective inner radius [L] pad effective outer radius [L] journal eccentricity [L] film thickness [L] rotor radius, top surface [L] wear particle size [L] system reference frame [L] pad etch depth [L] taper angle [  ] rotor axial position [L] journal eccentricity ratio [  ] rotor rotation angle [  ] dynamic viscosity [FTL  2] surface roughness [L] sector angle [ ] rotor angular velocity [T  1]

quick” gas feed connections are threaded into the top steel plate. The use of these fittings eliminates the potential for metallic debris during assembly, and the time required to connect the gas feed is substantially reduced. As in the Phase 1 test rig, the emitting end of an optical fiber is oriented perpendicular to the top surface of the rotor. As a tooth traverses the light path, a fraction of the light is reflected back into the optical fiber and back through the coupler to be picked up by the light meter via another optical fiber. The result is a fluctuating power signal as each tooth passes over the light path, which when transmitted to an oscilloscope determines the rotor speed. Fig. 8 shows the geometry of the assembled bearings in conformal and non-conformal configurations as defined previously [5,6] with the rotor positioned in contact with the thrust pad. A radial clearance parameter C0 is defined as C 0 ¼ r 1  R1 þ αðB  LÞ

ð1Þ

where a small, common axial taper α on rotor and hubs is a result of the DRIE etching process. In the conformal configuration, C0 is essentially constant over the entire clearance space, and in the nonconformal configuration C0 is the radial clearance at the top of the rotor. This radial clearance C0 is the kinematic limit of rotor translation in the x–y plane provided rotor and hub are axially aligned. A surface roughness value s1 ¼ 300 nm was measured on the hub channel walls (perpendicular to the channel flow) using a WYKO optical profilometer and validated using atomic force microscopy (AFM). A surface roughness value of s2 ¼100 nm was measured on the hub base which includes the thrust pads. Since rotor and hub employ the same fabrication process, the corresponding composite surface roughness sc of the contacting wall and thrust surfaces are given by ð2Þ1=2 s1 ¼ 424 nm and ð2Þ1=2 s2 ¼ 141 nm; respectively.

3. Experimental results A total of four test case studies, each with progressively larger clearances, were completed for microbearings in non-conformal (NC4, NC5) and conformal (C4, C5) configurations. Table 1 lists the dimensional bearing specifications for the case studies. Figs. 9 and 10 show the progression of wear for each of the four tests at a common number of cumulative cycles. Each test case was driven at a constant 68.80 kPa (gauge) gas supply pressure for a

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Fig. 2. Wear morphology of Phase 1 rotor surface.

Fig. 3. Exploded view of Phase 2 microbearing system.

Fig. 1. Phase 1 microbearing test system. (a) Assembled microbearing system (hub and rotor), (b) Hubs (pre- and post-drilled) and (c) Test fixture.

total of 2.5 million cycles. Optical images of the bearings in the test rig were taken with an Olympus MX50 optical microscope at 500,000 cycle intervals. The system remained in its assembled state for the entire test run of 2.5 million cycles. Micron-scale black particulates accumulated at the hub-rotor interface, and the rate of accumulation was initially greater in bearings with the larger nominal radial clearance, regardless of conformal and nonconformal configurations. The wear particles were also observed to be held in position by electrostatic forces generated between the glass cover slide and the silicon wafer. Table 2 shows the measured rotor speed (rev/min) at 500,000 cycle intervals. Note that the rotor speed increased for progressively larger clearance specifications, and for a given clearance specification, the speed remained essentially unchanged during the wear process.

Fig. 4. Phase 2 hub wafer.

Figs. 11 and 12 compare SEM micrographs of the disassembled hub and rotor bearing surfaces taken at initial (zero cycles) and at 2.5 million cycles. Striations on the rotor edges show evidence of

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Fig. 5. Thrust pads on Phase 2 hub wafer.

Fig. 8. Conformal (top) and non-conformal (bottom) bearing configurations.

Table 1 Test bearing system specifications. Rotor length Hub length Gas dynamic viscosity Surface roughness

L B μ

Δ N ψ0 P0 a b Wrotor

190 290 18 300 100 1.5 12 15 101 675 750 6.86

(mm) mm mPa-s nm (sidewalls) nm (thrust surfaces) mm

s

Pad etch depth Number of pads Pad sector angle Ambient pressure Effective pad inner radius Effective pad outer radius Rotor weight Test case

R1 (mm)

r1 (mm)

α (deg)

C0 (mm)

NC4 NC5

197.3 195.8

198.5 198.5

1.28 1.28

3.5 5.0

C4 C5

197.3 195.8

202.8 202.8

1.28 1.28

7.7 9.2

deg kPa (absolute) mm mm mN

Fig. 6. Phase 2 test apparatus—schematic.

Fig. 7. Phase 2 test apparatus—assembly.

rotor-hub impact, but the extent of impact damage is much smaller than observed previously [5]. In addition, a coating of nanometerscale particles have remained adhered by electrostatic attraction to portions of the rotor and hub surfaces. Fig. 13 shows a magnified view of the wear particulates on the top surface of the rotor at 2.5 million cycles. The particulates are observed to be micron-scale aggregates of near-spherical nanometer-scale particles. In the previous study [5], the amount of wear was quantified by measuring the shape of the conically-shaped damage profile on the rotor edges induced by rotor-hub impact. The lack of significant impact damage on the Phase 2 rotors requires a new method of quantifying wear. The optical microscope images of Figs. 9 and 10 are processed into binary (black and white pixels) images. The rotor surface area covered by wear debris Aw is calculated by counting the number of black pixels at each specified cycle interval and subtracting the black pixels observed at zero cycles. The volumetric wear V accumulated after a specified number of rotor cycles is estimated from the equation V¼ Aw tw, where tw is an assumed silicon wear particle size.

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Fig. 9. Phase 2 optical microscope images (non-conformal configuration, center hole diameter¼260 mm).

Based on the observed size of the particulates from the SEM micrograph of Fig. 13, each black pixel in the optical microscope images assumes a silicon particle size tw of 1 μm. The wear particles are generated on the cylindrical rotor and hub surfaces, transported between the top surface of the rotor and the glass

slide, and held in place by electrostatic attraction. This method of measuring wear is obviously very conservative, as it excludes wear particles which have accumulated at the bottom of the hub, attached to the sides of the rotor and hub surfaces, or have been transported out of view by the fluid dynamics of the gas stream.

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Fig. 10. Phase 2 optical microscope images (conformal configuration, center hole diameter¼260 mm).

4. Discussion As the channel air flow impinges on the rotor teeth, a staticallyequivalent radial load (in the system x–y plane of Fig. 8) and torque (about the system z axis) is transmitted from the rotor to the hub bearing surface. Both load and torque are generally dynamic

(time-dependent) due to tooth pattern motion in the channel flow field combined with loads induced from rotor imbalance. Fig. 14 shows one of a set of two-dimensional Fluent CFD models of the complete rotor and hub system. The rotor is fixed at a specified rotation angle θ, and the fluid region is modeled with approximately 96,000 cells. Measured supply pressure and zero

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(ambient) pressure boundary conditions are applied to the model channel inlet and outlet, respectively. No-slip impermeable boundary conditions are imposed on the hub and rotor surfaces. Fluid velocity and film pressure distributions are computed, from which rotor load components are obtained. The process is repeated for a discrete set of rotation angles between 0 and 22.5 degrees, representing the tooth-to-tooth periodicity of the system. Fig. 15 shows periodic time histories of rotor load components as a function of rotor angle obtained from the Fluent CFD simulation. Loads are transmitted from rotor to hub and are measured relative to the x–y computation frame of Fig. 14. The load magnitude, through variable, does not reverse direction, and

Table 2 Rotor speed (rev/min). Cycles

NC4

NC5

C4

C5

500,000 1,000,000 1,500,000 2,000,000 2,500,000

8,360 8,281 8,052 8,052 8,102

10,135 9,795 9,943 10,096 9,795

14,747 14,665 14,344 14,665 14,423

15,719 16,006 15,813 15,719 15,813

the average value of the load magnitude over the load cycle (1413 μN) is similar to that obtained with a simpler FLOTRAN single-tooth CFD modeling procedure employed with Phase 1 bearings [5,6] and discussed in Appendix B. For comparison with previously published wear studies involving silicon, we employ a mechanical wear model based on Archard's law [7] V¼

K Ls F 3H

ð2Þ

where K is the (dimensionless) wear coefficient, V is the measured volumetric wear (m3), F is the load magnitude (N), Ls is the length of the wear path (m), and H is the material hardness (N/m2). The load is taken from the Fluent CFD analysis, and an average measured hardness of 13 GPa for silicon is employed [8]. Fig. 16 shows the progression (as a function of the number of rotor cycles) of the measured wear coefficients for each of the four test cases. The wear coefficients remain relatively unchanged and fall within a relatively narrow band (between approximately 1  10  4 and 3  10  4) over the range of clearance specifications. These wear trends are quite similar to macroscale wear tests on polysilicon surfaces in ambient air with normal loads which are at least two orders of magnitude greater than used here [9].

Fig. 11. Phase 2 SEM images (non-conformal).

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65

Fig. 12. Phase 2 SEM images (conformal).

Fig. 13. SEM image of rotor (magnified).

The magnitude of the wear coefficients obtained here can be interpreted as a lower bound due to the conservative nature of the wear measurement, and with more careful particulate collection

methods, it is likely that the measured wear coefficients would likely fall in the 3.45  10  4 to 3.45  10  2 range reported for polysilicon at the macroscale [9]. Wear coefficient magnitudes and progression trends obtained here differ markedly from microscale testing of polysilicon structures reported elsewhere [7]. An electrostatic comb drive actuator provided reciprocating motion and loading of a thin polysilicon beam onto a fixed polysilicon post. The length scale of the wear region was on the order of 20 microns, the contact region between beam and post was on the order of a few microns, and normal loads were approximately two orders of magnitude smaller than employed here. The observed surface damage over time took on the form of V-shaped grooves on the beam indicative of abrasion wear, and the shape and depth of the wear grooves was measured using an atomic force microscopy (AFM) tip traversed through the groove. The magnitude of the wear coefficient decreased sharply from a short-cycle value of approximately 1.1  10  4 to less than 1  10  5 after approximately 1.8 million cycles. Although their method is also prone to uncertainty in their ability to accurately measure groove depth, the small length scales of their apparatus are on the order of the microstructural grain features of the polysilicon structure. The authors in [7] suggest that the wear resistance increases as the scale of the wear surfaces decreases to the micron scale. The length scale in our studies is approximately

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Fig. 14. Pressure distribution at θ¼ 14.5 degrees rotor tooth angle.

Fig. 16. Comparison of measured wear coefficients.

Fig. 15. Computed rotor loads from Fluent CFD analysis.

1000 μm based on the rotor circumference, and since our (very conservative) wear coefficient results correlate more closely with results obtained from macroscale testing, it is uncertain where this transition length scale lies.

5. Conclusions This paper has described a refinement of a test apparatus, denoted as Phase 2, to investigate the wear behavior of large aspect ratio silicon microbearing systems. Wafer dicing and drilling has been eliminated, allowing for a more rapid and reliable means of testing. Gas thrust pads in the hub base reduce the possibility of rotor to hub base contact and promotes stability, which is a plausible explanation for the observed reduction of impact damage. Measured wear coefficients based on the Archard relation and using a novel but conservative method of measuring wear correlate more closely with published values obtained with macro-scale test fixtures.

Acknowledgments This work was supported by grants through the Department of Energy, Office of Biological and Environmental Research (DE-FG0202ER63393) and the National Science Foundation, Materials Design and Surface Engineering Program (CMMI-0409557) and Major Research Instrumentation Program (ECS-0619676). This work was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765).

Appendix A. Gas film bearing loads Thrust pads Fig. A1 shows a schematic of the rotor which rotates at a constant angular velocity ω and is supported by N equally spaced

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Fig. A2. Thrust bearing load capacity: Phase 2 microbearing.

Fig. A1. Thrust pad geometry.

stepped sector thrust pads. Each thrust pad has spatially constant film thickness values h1 and h2 in corresponding bearing regions I and II, respectively, where h1 4h2. Each bearing region subtends a common angle ψ0 ¼ π/N. The rotor covers only a portion of the pad, such that the effective inner and outer bearing radii a and b are defined by the pad inner radius and rotor outer radius, respectively. Each pad has a common etch depth Δ in region I, so that h1 ¼h2 þ Δ. Assuming incompressible flow and ambient pressure boundary conditions along the pad edges, the film load W is given by [10] 1

W ¼ 12N μω½ lnðb=aÞ3 ðh1  h2 Þ ∑ SðnÞ n¼1

ðA1Þ The incompressibility assumption for the gas film requires [11]

where ( SðnÞ ¼

Fig. A3. Journal bearing schematic.

ð  1Þn þ 1 b þa2 2

)2

ðnπ Þ2 þ ½2 lnðb=aÞ2

β T1 T2

ðA2Þ

with T 1 ¼ 2 tanh ½ nπψ 0 = ln ðb=aÞ2 

3μωða þ bÞ2 ψ 0 2P 0 Δ

2

o1

ðA5Þ

where P0 is ambient absolute pressure. For the tested rotors over the measured speed range, β ranges from 0.05 to 0.1, which strongly supports the use of an incompressible gas film model in the load calculations.

ðA3Þ Journal bearing

3 3 T 2 ¼ ðh1 þ h2 Þcoth

½nπψ 0 = lnðb=aÞ

ðA4Þ

The series expansion in Eq. (A1) is rapidly convergent; twenty terms in the series are found to be sufficient. Fig. A2 shows film load W as a function of film thickness h2 over the range of rotor speeds reported in this paper. Full hydrodynamic lubrication is attained when h2 E 3sc ¼ 423 nm, where sc ¼141 nm is the composite roughness of the hub and rotor thrust surfaces. When the film load equals the rotor weight Wrotor listed in Table 1, the resulting value of h2 falls within a full-film lubrication regime over the measured speed range provided in Table 2 (8000–16,000 rev/min).

Fig. A3 shows a schematic of the microbearing rotor with uniform clearance C which rotates at a constant angular velocity ω and is subjected to a constant radial load F. Under steady load and speed, the rotor center will assume a constant eccentricity e relative to the hub center. (This result precludes potential stability problems attributed to rotor inertia.) The load calculated by the CFD analysis as shown in Fig. 15 is not steady, but the load variability is small enough to employ its average value in the analysis which follows. For a fixed eccentricity ratio magnitude ε ¼|e|/C ¼0.8, the load magnitude F is given by [10] F ¼ 12LRμωðR=CÞ2 =π

ðA6Þ

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S. Demiri et al. / Wear 312 (2014) 58–69

Fig. A4. Journal bearing film load capacity: Phase 2 microbearing.

Fig. B2. Pressure distribution: Phase 2 single-tooth CFD model.

Fig. B1. Phase 2 single-tooth CFD model (not to scale, dimensions in μm).

where R is the nominal rotor radius. The load–speed linearity relationship which assumes gas incompressibility holds for

ω o P 0 =½6μðR=CÞ2 

ðA7Þ

At speeds above the threshold value provided in Eq. (A7), compressibility effects become prominent and the linear load– speed relation no longer applies. For each radial clearance specification, the minimum film thickness hmin for a specified eccentricity ratio ε can be found from hmin ¼ Cð1  εÞ

ðA8Þ

Fig. A4 shows predicted film load F as a function of rotor speed for a family of radial clearance specifications employed in the experimental studies. Each curve extends to the threshold speed value given in Eq. (A7). It is observed that the film load stays well below the apply load Frotor ¼1413 μN even at rotor speeds which are substantially greater than the tested range and for minimum film thickness values which are well below the 3sc ¼1272 nm threshold for full-film lubrication, based on a composite roughness value sc ¼424 nm for the rotor and hub cylindrical surfaces. The rotor thus operates in a boundary lubrication regime for the rotor and hub cylindrical surfaces. Appendix B. Single-tooth CFD analysis Fig. B1 shows a two-dimensional CFD model of the Phase 2 system which corresponds to the instant when one of the hub teeth is parallel to the channel flow. The model takes into account turbulence (via a standard k-ε model) and approximates the channel flow as two-

dimensional parallel to the system x–y plane. No-slip impermeable boundary conditions are imposed on the channel walls, and velocity boundary conditions (in the system x-direction only) based on measured rotor speed are imposed on surfaces representing the moving tooth and rotor outer diameter. The model employs fournoded isoparametric two-dimensional ANSYS FLOTRAN FLUID141 finite elements. Measured supply pressure and zero (ambient) pressure boundary conditions are applied to the model channel inlet and outlet, respectively. Fig. B2 shows the pressure field with 9882 rev/min rotor speed and 68.80 kPa gas supply (gauge) pressure. Pressure distributions on leading and trailing tooth faces are observed to be essentially uniform except, as expected, near the tooth tip. Average leading and trailing face pressure values of 51,791 and 19,692 N/m2, respectively, when integrated over the respective tooth surfaces yield a resultant tooth load of 1220 μN which is quite similar to the 1413 μN value obtained from a CFD analysis of a complete rotor-hub system. The load results were also found to be essentially independent of rotor speed as expected due to the relatively low tooth linear velocities.

References [1] K.E. Peterson, Silicon as a mechanical material, Proc. IEEE 70 (1982) 420–457. [2] D.M. Tanner, J.A. Walraven, L.W. Irwin, M.T. Dugger, N.F. Smith, W.P. Eaton, W.M. Miller, S.L. Miller, The effect of humidity on the reliability of a surface micromachined microengine, in: Proceedings of the 1999 IEEE International Reliability Physics Symposium, 1999, pp. 189–197. [3] K. Breuer, F. Ehrich, L. Frechette, S. Jacobson, C.-C. Lin, D.J. Orr, E. Piekos, N. Savoulides, C.-W. Wong, Challenges for lubrication in high speed MEMS, in: Hsu, Ying (Eds.), Nanotribology, 2003. [4] D. Kim, D. Cao, M.D. Bryant, M. Meng, F.F. Ling, Tribological study of microbearings for MEMS applications, J. Tribol. 127 (2005) 537–547. [5] S. Demiri, S. Boedo, W.J. Grande, Conformality effects on the wear of lowspeed, large aspect ratio silicon journal microbearings, Wear 268 (2010) 361–372. [6] S. Demiri, Geometric Effects on the Wear of Microfabricated Silicon Journal Bearings, Ph.D. Thesis, Rochester Institute of Technology, Rochester, NY, 2010. [7] D.H. Alsem, M.T. Dugger, E.A. Stach, R.O. Ritchie, Micron-scale friction and sliding wear of polycrystalline silicon thin structural films in ambient air, J. Microelectromech. Syst. 17 (2008) 1144–1154.

S. Demiri et al. / Wear 312 (2014) 58–69

[8] L.J. Vandeperre, F. Giuliani, S.L. Lloyd, W.J. Clegg, The hardness of silicon and germanium, Acta Mater. 55 (2007) 6307–6315. [9] M.N. Gardos, Tribological behavior of polycrystalline and single-crystal silicon, Tribol. Lett. 2 (1996) 355–373.

69

[10] O. Pinkus, B. Sternlicht, Theory of Hydrodynamic Lubrication, McGraw-Hill, New York (1961) 120–121. [11] K.C. Kochi, Characteristics of a self-lubricated stepped thrust pad of infinite width with compressible lubricant, J. Basic Eng. 81 (1959) 135–146.