Suplimental Information
Experimental Section
The testing suite consists of an optical displacement sensor (ODS) (Philtec D6-H1), two
pressure transducers (Omega PX26-005DV), and a mass flow controller (MKS Instruments RS-485).
LabVIEW software is used so that these components are able to work together. A spindown test is as
follows: The thrust flow is first set to a predetermined load give load range and what the equivalent
pressure measurement is. Then actuated flow is enabled up to 6–8 SLM accelerating the rotor to 20
krpm. The actuated flow is then deactivated, allowing the rotor to decelerate only under the influence
of system friction. During the rotor deceleration, the angular position of the rotor is recorded through
periodic pulses derived from the 12 equi-radial tracking petals interacting with light from the optical
displacement sensor. This test procedure is repeated in rotor normal load increments of 5–7.5 mN
increasing to then decreasing from 100 mN. Angular position during spin-down is measured via
the optical displacement sensor. The spin-down angular position data is first fit to the
equation,
𝜃 = 𝐴(1 − 𝑒 −𝐵𝑡 )
(S1)
Where 𝜽 is angular position, t is time, and A and B are fitting coefficients. Therefore angular
acceleration (𝜽̈) and velocity (𝜽̇) are related as,
𝜃̈ = −𝐵𝜃̇
(S2)
𝜏 = 𝐼𝜃̈
(S3)
And torque is,
where I is the mass moment of inertia for the rotor-ball system which for calculations is
assumed to be a silicon disc with a torus of the same mass of the balls, and 𝝉 is friction torque.
Therefore DFT is given as,
𝜏
(S4)
=𝐼∙𝐵
̇𝜃
With the B value coming from the original curve fit. Dynamic Friction Force is therefore DFT
𝐷𝐹𝑇 =
divided by the radius of the microturbine raceway. Hertzian contact mechanics are used to
calculate
contact pressure, contact area, and deformation. Hertzian contact makes a number of
assumptions, including: elastic strain below the strain limit of the contacting bodies, friction-less
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contact, surfaces are continuous and non-conforming, and the areas of contact are significantly smaller
than the characteristic lengths of the body.
The two-stage vapor lubrication system comprises of a tank of de-ionized water filled up
to 30–35% capacity, which saturates N2 gas flowing into it. The second stage consists of a
condenser tank, which condenses out non-equilibrium water from entering the device. The
partial pressure of the system is controlled through a pressure regulator (Norgren R07-100RGEA) attached after the N2 source. The relative saturation is determined by a hygrometer
(Omega RH82) before the gas enters the device. For example, if the pressure regulator is at
10 psi at room temperature, the relative saturation is 18% at the output. Geometric
characterization of wear is performed by using an optical profilometer (Veeco WYKO
NT1100). EDS is carried out using a scanning electron microscope (Hitachi SU-70).
Testing Platform Fabrication
The silicon microturbine used for microball bearing characterization consisted of three
chips fabricated from single-crystal Si <100>, 0.5 mm thickness. 440C stainless steel balls,
diameter 285 or 500 μm, support a 10-mm, free-rotating silicon rotor. The Si rotor-stator
structure is composed of eutectically bonded chips with internal etched features to encapsulate
various numbers of balls and external features for actuation (turbine) and measurement
(petals). All Si features are created by deep-reactive ion etching of Si in sulfur hexfluoride
(SF6) plasma chemistry. Microturbine blades, vanes, and displacement measurement petals
are 250 μm tall. Devices using 285-μm-diameter balls use rectangular-cross section trenches
of 195 and 95 μm deep to serve as the internal structures comprising the raceway. Devices
using 500-μm-diameter balls use 310 and 205 μm deep etches to serve the same purpose. A Si
chip with center and peripheral through-holes is used to direct external gas flow through the
turbine structures. A complete fabrication procedure has been previously described in [15].
The microturbine was packaged between machined acrylic plates with pressure sensing and
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flow ports, sealed with rubber o-rings. The device is periodically cleaned in acetonemethanol-isopropanol solutions under ultrasonic excitation.
Error Calculation
The error in the spin-down data primarily comes from three places: 1) the pressure
transducer used to measure the backside pressure from which the normal load is calculated, 2)
the position data obtained from the optical displacement sensor, and 3) the quality of the
curve fit to the position data. The PX26-001DV pressure transducer from Omega Engineering
used to measure the thrust pressure of the thrust cavity, from which normal force was
calculated had a range of ±1psi, and is reported to have ±0.3% full scale repeatability. This
equates to an error in calculated normal force of 1 mN. The optical displacement sensor
operates at 20 kHz, so at 10,000 rpm with 12 etched tracking marks, five measurements are
taken in each peak and valley. This equates to a maximum error of 5 milliradians in locating
the tracking mark interface. Considering the device spins down through hundreds of radians,
this error is negligible. The change from peak-to-valley sensing improves drastically as the
device decelerates. This method assumes a constant deceleration between measurements of
the edge of tracking marks. Additional error comes from the quality of the curve fit of the
position data. The position data is fit to a power-law where the second derivative of the
position data equals a constant times the first derivative, therefore implying a linear
relationship between speed and friction, as observed in the linear test devices. This allows for
speed to be taken into account in the value of friction torque. Curve fit qualities are r2>0.98.
Additional error in the DFT measurements comes from the influence of the thrust plenum
flow, used to impart normal load on the rotor. Thrust flow leaks through the bearings and
exits through the rotor blades, imparting some torque opposing friction. An estimate of the
added torque using conservation of momentum shows that at during the initial stages of the
spin-down test, the thrust flow leak contributes 5% at 10,000 rpm and quickly drops off to
0.0001% at 1,000 rpm.
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Finally, there is uncertainty from unintended variation amongst the geometries of the
microturbines. These variations include minor changes to raceway waviness, differences in
surface roughness caused by micro-masking during the raceway etch steps, and variation in
the raceway sidewall quality. To establish the uncertainty from geometrical differences, three
microturbines of the 285, high variation were tested at a set normal load and the standard
deviation amongst observed friction was established. It was found that this variation is about 1
x 10-10 N·m/rpm.
Abstract image:
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