Lubricant Free Foil Bearings Pave Way to Highly Efficient ...

LUBRICANT FREE FOIL BEARINGS PAVE WAY TO HIGHLY EFFICIENT AND RELIABLE FLYWHEEL ENERGY STORAGE SYSTEM

Hooshang Heshmat, Ph.D. Mohawk Innovative Technology, Inc.

Albany, NY, USA

James F. Walton II Mohawk Innovative Technology, Inc.

Albany, NY, USA

ABSTRACT Advanced compliant foil bearings capable of operating in

low ambient pressures associated with soft vacuum are now

paving the way to a new type of flywheel energy storage

system. Many conventional flywheel energy storage system

design approaches use active magnetic bearings with backup

bearing technologies to meet the need for high speed operation

in a low ambient pressure environment. Low ambient pressures

are needed to overcome the power loss limitations associated

with windage at high surface speeds. However, bearing

technologies that rely on active control tend to be large, are

dynamically soft which necessitates backup bearings and

require a power supply which consumes some of the stored

power to maintain rotor levitation.

In this paper the authors will demonstrate both

theoretically and experimentally the ability of advanced 5th

generation compliant foil bearings to support large flywheel

rotors weighing in excess of 900 N and which can operate to

speeds in excess of 40,000 rpm. Testing conducted at pressures

as low as 7 kPa demonstrates the ability of foil bearings to

operate in low ambient pressures consistent with flywheel

energy storage system needs for low windage loss. The authors

will also present a hypothesis and the mechanisms involved in a

hydrodynamic phenomenon that allows a foil bearing to operate

successfully when the mean free path of the air molecules is

exceedingly large due to low ambient pressures.

INTRODUCTION Ever since the first electricity generating facility was

put into practical use energy storage solutions have been sought

to provide a more reliable and resilient infrastructure. The need

for energy storage is increasing to support continuous

operations in the event of power interruptions especially in

industrial processes that demand reliable power such as the

semiconductor industry. While peaking generators, which are

turned on to compensate for electricity shortages, are designed

to meet longer duration energy demands, they are expensive to

operate and require time to begin producing electricity. As

more solar and wind power plants are constructed energy

storage approaches to compensate for the variable/intermittent

nature of these sources are being used, among them batteries,

compressed air energy storage, pumped hydro and flywheels.

Flywheels are electromechanical devices that store energy

in the form of kinetic rotational energy for subsequent

conversion to electrical energy. Most modern flywheel energy

storage systems (FESS) consist of a large diameter composite

wheel supported on electromagnetic bearings operating in a

vacuum. The amount of energy stored in a flywheel is

proportional to the inertia and the square of the velocity, thus

high speed is the most effective means of increasing the amount

of stored energy. However, to maximize flywheel efficiency

one needs to ensure that the inherent electrical and mechanical

losses are minimized. While electric machine loss mechanisms

include the conductors and laminated cores, it is flywheel

windage and bearing losses due to the high operating speeds

that can most adversely affect system efficiency and are the

focus of this paper.

Windage loss in a motor/generator is the power absorbed

by the fluid surrounding the rotor as a result of the relative

motion between the rotor and the stator. Since this power must

be overcome and is not converted into useful energy, the

presence of windage loss decreases the overall efficiency of the

machine. Another undesirable characteristic of windage loss,

Proceedings of the ASME 2016 10th International Conference on Energy Sustainability ES2016

June 26-30, 2016, Charlotte, North Carolina

ES2016-59350

1 Copyright © 2016 by ASME

and sometimes the most important, is that the power absorbed

is converted into heat, which increases the temperature of the

rotor. Such temperature increases can reduce the composite

material strength while also reducing the motor/generator

permanent magnet properties.

The flow of fluid between two rotating concentric

cylinders, such as in motors and generators has attracted the

interest of the giants of science for centuries, including Stokes,

Rayleigh, Couette, Taylor, and many more since the magnitude

of these losses can become increasingly large with increasing

speed and especially in the narrow rotor-stator gaps or locations

where the flow is typically turbulent. As the Reynolds Number

(Eq. 1) increases, the flow becomes particularly complex and

undergoes a series of transitions from circular Couette flow, to

axially periodic Taylor vortex flow [2], to a state with waves on

the vortices [3], to turbulent Taylor flow [4]. In its simplest

form, Taylor-Couette flow arises from the shear flow between a

rotating inner cylinder and a concentric, fixed outer cylinder.

The stable flow for this geometry is known as cylindrical

Couette flow in which the flow is driven by the motion of one

wall bounding a viscous fluid. Cylindrical Couette flow

becomes unstable as the rotational speed of the inner cylinder

increases (i.e., at Taylor Number (Eq. 2) >41.3), causing first

axisymmetric toroidal vortices (i.e., 41.3<Taylor Number <400)

and finally turbulent flow (Taylor Number > 400). Where

Reynolds Number (Re) and Taylor Number (Ta) are defined as:

Re = ρ ω R h / μ (1)

Ta = R ω h / (υ (d/R)½) (2)

While the above are used as a reference, it should be noted

that Schlicting [4] indicates that turbulent flow does not

necessarily become well developed until Taylor and Reynolds

Numbers vastly exceed the limit of stability. Typically, it is not

until Ta exceeds 1715 (Re > 3960) that fully turbulent flow is

encountered for the case where the inner cylinder rotates within

a non-rotating outer cylinder.

Numerous studies have been conducted to evaluate

windage losses directed at high-speed machines, such as

motor/generators. For example, Vranick [6] developed a first

approximation windage loss model that included both laminar

turbulent flow. Gorland and Kempke [7-8] used a simplified

drag model when evaluating smooth Lundell alternators at high

Reynolds numbers, Wild et al. [9] performed experimental and

computational investigations of windage losses between

rotating cylinders and Golding et al. [10] presented a method

for modeling windage losses in the turbulent flow regime for

close clearance cylinders. Durkin and Schauer [11] performed

a parametric analysis of the effect of various rotor, stator and

air gap geometries on windage losses in alternators/generators.

In calculating windage losses, Durkin and Schauer used one

relation for coefficient of drag based on the Taylor number.

Saint Raymond et al. [12], used an approach similar to Durkin

and Schauer to determine windage loss of a smooth rotor

supported by magnetic bearings. In most of these cases, the

analysis developed and investigations conducted were for

smooth cylinders or it was assumed that operation in the

turbulent regime (i.e., Re < 41.1(R/h)½ ) [16] would not be

greatly affected by additional surface irregularities. However,

many machines are designed with, or in operation may not be,

cylindrical but rather have non cylindrical shape. Surface

roughness may also vary, both for the rotor and stator. As such,

in addition to investigating rotor gap, length and ambient

pressure in the rotor system, it is essential that the effects of

rotor shape, surface roughness and stator inner diameter surface

be more fully examined and methods to reliably account for

them be developed. Recent experiments of Closed Brayton

Cycle systems with a close clearance between stator and rotor,

as conducted at high pressures by Bruckner, Howard, et al. and

Wright, et al., showed reasonably good correlation when using

a Taylor-Couette flow model [13,14,15].

In the present work however, the authors are examining

lower pressure or soft vacuum regimes that may be used in

flywheel systems to demonstrate that foil bearings can

potentially be used instead of magnetic bearings with positive

effect. Magnetic bearings offer many positive attributes

including the ability to tune response to reduce vibrations at

specific frequencies, auto-balance, eliminate lubrication

systems and the corresponding maintenance and loss issues,

and being non-contact offer very long life. However, magnetic

bearings also require backup or auxiliary bearings in the event

of potential failure of either sensors or power electronics and

are by design “soft” dynamically, which requires special

considerations to accommodate transient impact/shock events

[16].

COMPLIANT FOIL BEARINGS

One of the essential features of a Compliant Surface Foil

Bearing (CSFB) is that it possesses a two-fold mechanism

combining structural elasticity and hydrodynamic pressure

forces to produce bearing stiffness and damping. The elasticity

mechanism is via the geometry and the materials used for the

compliant structural support elements and the smooth top foil,

which combine to provide the compliant bearing surface

support [17-24]. The other mechanism is hydrodynamic,

resulting from the gas film between the shaft and the smooth

top foil. As shown in Figure 1, a single top foil may be used to

extend around the bearing circumference, forming the

equivalent of a full hydrodynamic bearing in a simple and

compact configuration. Alternatively, multiple pads and

smooth top foils may be used to form the bearing surface. The

compliant surface support structure is made of corrugated bump

elements, which can be manipulated to provide the bearing

stiffness needed to meet specific system dynamic requirements.

In CSFBs, the clearance geometry required to generate

load-carrying hydrodynamic films is provided by the elastic

deflection of the foils. As speed increases, the smooth top foil


and corrugated support foils are automatically forced radially

outward under the influence of the generated hydrodynamic

pressure, enhancing formation of the converging wedge. Thus

the optimum shape for hydrodynamic action is formed without

having to use complex and expensive machining. Furthermore,

the converging effects become more pronounced as a function

of speed and load, thereby, increasing bearing load capacity.

With the nomenclature of CSFB as given in Figure 1, the

two-dimensional compressible Reynolds equation can be

written as: 1

𝑅2 𝜕

𝜕𝜃 [ℎ3𝜌

𝜕𝑝

𝜕𝜃] +

𝜕

𝜕𝑧 [ℎ3𝜌

𝜕𝑝

𝜕𝑧] = 6𝜇𝜔

𝜕𝜌ℎ

𝜕𝜃 (3)

However, the density is related to the pressure by an

equation of state, generally of the form:

𝑝 = 𝐶𝑔𝜌𝑛 (4)

Where Cg is a constant, n=1 for isothermal conditions and

n = γ = Cp/Cv for adiabatic conditions. The usual situation with

a gas bearing is approximated by the isothermal case so it will

be assumed in further analysis that p = ρCg and considering the

following non-dimensional parameters:

�̅� = (𝑍 𝑅⁄ ); �̅� = (𝑝 𝑝𝑎⁄ ); ℎ̅ = (ℎ 𝐶⁄ );

Λ = 6𝜇𝜔

𝑝𝑎 (

𝑅

𝐶)

2

Normalizing Reynolds equation (3), we obtain

𝜕

𝜕𝜃[�̅�ℎ̅3 𝜕�̅�

𝜕𝜃] +

𝜕

𝜕�̅�[�̅�ℎ̅3 𝜕�̅�

𝜕�̅�] = Λ

∂

∂θ (�̅� ℎ̅) (5)

The film thickness variation h(𝜃) is that due both to

eccentricity (e) and to the deflection of the foil under the

imposed hydrodynamic pressures. Since the latter is

proportional to the local pressure we have

ℎ = 𝐶 + 𝑒 cos(𝜃 − 𝜑0) + 𝐾1 (𝑝 − 𝑝𝑎) (6)

where K1 is a constant reflecting the structural rigidity of

the bumps and is given by

𝐾1 = (𝛼 𝐶

𝑃𝑎) (7)

Where 𝛼 = 2 𝑆 𝑃𝑎

𝐶𝐸 (

𝑙0

𝑡)

3

(1 − 𝜈2) is the compliance of the

bearing and the quantities s, l0 and t are the bump pitch, bump

width and foil thickness respectively. After having solved for

𝑝(𝜃, 𝑧) with the appropriate pressure boundary conditions, one

can then determine bearing reaction forces and correspondingly

normalized load capacity �̅� where

�̅� = 𝑊

𝑃𝑎 𝑅2 (8)

Given that the finite difference solution to Reynolds

Equation accounts for discrete and decoupled stiffness elements

at each node (i.e., the local stiffness does not contribute to its

neighbors stiffness), some means is needed to include the

influence of the top smooth foil in the solution of the pressure

field and correspondingly the bearing load capacity. The

diagram in Figure 2 presents the program logic flow chart for

the analysis that solves Reynolds equation for CSFBs with

compressible gas, including the contribution of not only the

compliant structural bump foils but also the top smooth foil as

developed by Heshmat [25]. The static force-displacement

relationship plays an important role in analyzing CSFBs, as the

compliance of the surface governs the operational

characteristics. The solution of the governing hydrodynamic

equations must deal with a compressible fluid that is coupled

with a compliant bearing surface. A solution to the structural

compliance is provided in two stages. In formulating the first

level elasticity solution of the compliant element stiffness

matrix, it is assumed that the smooth top foil follows the global

deflection of the backing springs and will not follow the

indentation between bumps of the corrugated backing springs.

It is also assumed that deflection of the top foil and backing

springs, in responding to the hydrodynamic pressure, is

dependent on local effects only. The film thickness variation is

due both to initial geometry (eccentricity and initial surface

shape) and the deflection of the compliant surface under

imposed hydrodynamic pressure. The two-dimensional

compressible Reynolds equation is written in finite difference

form with the dependent variable represented by a finite

number of points located at intersections of a grid mesh. The

resultant form is linearized by the Newton-Raphson method,

represented in matrix notation and solved by the column

method to satisfy boundary conditions. The resultant pressure

field is then taken to the next level of elasticity analysis via

finite element analysis to include the effects of the top smooth

foil in the CSFB analysis. In this higher level elasticity

analysis, the mathematical model of the foil bearing consists of

a staggered, thin top foil supported via springs subjected to the

pressure field. The combined top foil and backing spring

Figure 1 Complaint Surface Foil Bearing schematic diagram and coordinate system

X

Y

SmoothTop Foil

BearingCasing

Backing SpringCorrugated/Bump Strip Free End

Corrugated/BumpStrip Fixed End

ω

φ0

θs

o

o e

θ2

θe

θ1

θ

96-005215-002

Shaft


deflection is computed for the given pressure, resulting in a

deflection matrix and overall structural stiffness.

Using this coupled elasto-hydrodynamic procedure with

3-D Finite Element Analysis of the top foil modeled with shell

elements supported by springs along the bottom surface with

separation and sliding at the contact elements, one can then take

into account the influence of both top foil and supporting spring

elements on the generated pressures in the bearing. Figure 3

shows journal foil bearing pressure profile for one-half of the

bearing length (maximum centerline pressure peaks shown at

the bottom of the figure. From the developed pressure, load

capacity and bearing stiffness can be determined. The 76 mm

diameter by 102 mm long journal foil bearing pressure profile

is for an operating speed of 30,000 rpm under a static loading

of approximately 178 N. The resulting nominal minimum film

height was predicted to be 0.021 mm.

Figure 3 Generated pressure profiles for foil journal bearing

For a practical flywheel energy storage system hardware

demonstrator such as shown in Figure 4 in which a 94.5 kg

(208 lb) rotor was designed to be supported on foil gas bearing

operating in “soft” vacuum of approximately 7-to-10 kPa one

might prefer to assess bearing performance as a function of

ambient pressure rather than Λ. In the example flywheel

system, the most heavily loaded foil journal bearing

experiences approximately 50 kgf or 495N (111 lbf) static load.

For bearing dimensions of 102 mm in length by 76 mm in

diameter, the resulting bearing static pressure loading is

approximately 64 kPa (9.25 psi). Figure 5 shows that as

ambient pressure decreases, both nominal minimum film height

and bearing load carrying capacity decrease to a level less than

necessary to support the rotor weight. At an ambient pressure

of 101 kPa bearing load capacity is predicted to be 495 N and

that minimum film height will be 25 micron. However, at an

ambient pressure of 4.5 kPa, load capacity drops to 33 N which

would result in a minimum film height of 15.6 micron. Yet the

bearings do support the rotor weight. The hypothesis is

therefore put forth that there is a morphological mechanism that

combines hydrodynamic and quasi-hydrodynamic third body

lubrication effects to support the rotor. In fact, it is

hypothesized that both hydrodynamic and morphological

effects are at work in all gas foil bearing operating conditions, it

Figure 2 Foil bearing analysis calculation procedure

Figure 4 High-speed flywheel demonstrator system built for operation in "soft" vacuum

Initial Geometry [gij]Int

Boundary & Operating Conditions

Calculate Initial Structural Element Compliance

[αij]Int

from Close-Form Elasticity Solution

Apply Local Pressure (Default) - Deflection Relation

hij ~ [gij]Int

+ [αij]Int

[Pij]Default

Hydrodynamic Analysis:

Linearized Finite Difference with Variable Grid

Solve for Pressure [Pij]

Accuracy Check

Convergence Check

[Pij]New

≈ [Pij]Old

Compliancy Check

Structural Finite Element Analysis:

Combine Top Foil & Backing Springs

Compute Top Foil Deflection δij due to [Pij]

Generate Influence Coefficient [Cij]

Modify Bearing [gij]New

Geometry

Determine Film Thickness

hij ~ [gij]New

+ [Cij] [Pij]

Top Foil Influence Factor

[Rij] = [αij] / [Cij]Final

Final Outcome W, ε, φ

Convergent

Not Convergent

1st Iteration &

[Pij]Old Not Existing


is just the ratio of these two that vary as shown in Figure 6.

With thick film operation, the hydrodynamic effects dominate

and are produced in a lubricant by the relative motion of the

tribosurfaces. While the lubricant is typically either oil or gas,

the lubricant can be any appropriately sized third-body located

in the bearing clearance that is not integral with either surface.

In such a case, the bearing clearance could be filled with mixed

gas/dry powder particulates, either directly fed to the bearing

clearance or generated from prepared “pellets” that may rub on

the shaft. Heshmat [26] previously demonstrated pelletized

powder lubricated with a 100 mm powder lubricated rigid pad

bearing system that operated for an hour with a shaft spinning

at 30,000 rpm.

Figure 5 Foil bearing load carrying capacity and film height as a function of ambient pressure

Figure 6 Contribution of hydrodynamic and morphological elements in tribological processes

In compliant foil gas lubricated bearings, as the film

becomes thinner, the gas hydrodynamic effects become less

dominant and the morphological effects provide greater

contribution to bearing load capacity. The morphological

effects are due to the elastic, plastic, chemical, molecular,

debris and other surface phenomena (e.g., roughness, porosity,

etc.) in the zone of the interface contact and are governed by

the quasi-continuum model [27-30]. Thus, for thick gas films,

the hydrodynamic effects will dominate and morphological

effects will be present but with a small percentage effect.

Correspondingly, under very thin film conditions, the

morphological effects will dominate, especially where the film

is so small that asperity to asperity contact is likely and wear

debris generated.

In the present case, the reduction in film height is due to

low ambient pressures. The standard requirement in

hydrodynamic bearings is for the fluid film to have, at its

boundaries, the same velocity as the adjacent surfaces. This,

however, is true for flows where the molecular mean free path

of the gas (ℓ) is much smaller than the film thickness. Gas

bearings generally have thick films and the foregoing does not

always hold. If the mean free molecular path becomes

comparable to hmin, the ability of neighboring molecules to

“drag” adjacent molecules into the converging bearing gap is

diminished and there will be slip at the boundaries. Thus, a

new parameter enters the governing hydrodynamic equations

[27].

𝒮ℬ = (ℓ

ℎ𝑚𝑖𝑛(𝑛𝑜𝑚𝑖𝑛𝑎𝑙)) =

𝑀𝑒𝑎𝑛 𝐹𝑟𝑒𝑒 𝑃𝑎𝑡ℎ

𝐹𝑖𝑙𝑚 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 (9)

Namely, if 𝒮ℬ becomes equal or greater than one (1), the

load which is carried with the fluid film drastically decreases

and high speed rub may dominate the dynamic process if there

are no other tribological means to share the bearing load. We

see in Figure 7 that, as ambient pressure decreases, we reach a

point where 𝒮ℬ becomes greater than one (1) slip would be

expected to occur while at the same time a maximal or

optimum bearing pressure ratio is predicted. This maxima or

optimal pressure ratio (Pr) is due, primarily, to the compliancy

built into the foil bearing and which accommodates generated

bearing pressures. Even though an optimal bearing pressure

ratio may be achieved both load capacity and film height are

greatly reduced. Given these conditions of low load capacity

and small minimum film height, one would expect that rubbing

between shaft and bearing would occur. However, if one

considers the morphological effects and third body particulate

in the clearance, increased load carrying capacity is possible

through an apparent increase in viscosity of the gas/particulate

mixture in the gap.

Figure 7 Identification of starved lubrication region with slip at

the boundary as a function of ambient pressure


If the resultant wear particle generation during asperity

contact produces a mixture of particles and gas molecules a

model to describe the effective rheological properties that will

be experienced by the bearing is needed. As such, the

following discussion is presented:

It is well known that the earliest theoretical work on the

effective viscosity was due to Einstein [31], whose derivation

led to the effective viscosity of a mixture for dilute suspensions

of spherical particles to be linearly related to the particle

concentration as follows:

𝜇𝑟 = 1 + 2.5 𝜑𝑝 (10)

Where μr = μm /μf the relative viscosity and is defined as

the ratio of the effective viscosity of the particle-fluid mixture

(μm) to the viscosity of the fluid (μf), and φp is the volumetric

concentration of the particles. However, Einstein's viscosity

equation assumes that fluid viscous effects dominate and the

influence of particle interactions are not considered, hence, the

validity of this formulation cannot be extended to solid

concentrations of order 2% or higher [32].

Following Einstein’s work, numerous expressions have

been proposed to extend the range of validity to higher

concentrations. They are either theoretical expansions of

equation (10) to higher order in fp or empirical expressions

based on experimental data. For example, Vand [33] extended

Einstein’s work, taking into account particle concentration,

proximity of walls and particle interactions to develop the

following equation:

ln 𝜇𝑚 = (2.5 𝜑+2.7 𝜑2

1−0.61 𝜑) (11)

Plots of the theoretical and experimental values of

intrinsic viscosity for solid particles suspensions in a fluid

medium according to Vand are presented in Figure 8.

While the Einstein and Vand models were initially

developed for liquid particle mixtures, additional research has

also been conducted giving credence to the use of a mixed

gas/particle viscosity as reported in [34-37]. Heshmat

measured viscosity of several powders of different sizes (1-2

and 5-6 micron) poured into a viscometer previously calibrated

with oil lubricants to verify the validity of the viscometer

measurements.

To determine possible gaseous mixture viscosity particle

packing density was estimated as follows. In a tightly packed

spherical particles under minimal external packing pressure, the

solids fraction 𝜙 is

𝜙 = [(43⁄ ) 𝜋 𝑅3] (8 𝑅3) = 𝜋

6 ⁄⁄ = 52.4% (12)

Therefore, the inter-spacing gaps or unoccupied space

between the particles amounts to about 47.6%.

When considering instances where high speed contact

takes place between a shaft and foil with a surface coating

tailored to produce small specifically sized particulates such as

with Korolon®, the value of 𝜙 may approach the maximum of

52.4% due to the compression in the loaded region of contact.

Figure 8 Theoretical and experimental values of viscosity of slurry mixture as a function of solid fraction

Experimental data, taken from Heshmat [26], shows a

solid fraction of approximately 31% to 35% percent for fine

particle TiO2 powder. For this range of 𝜙, and based on

correlation with Einstein and Vand (see Figure 8), the relative

viscosity was estimated to be µR =1.15 CP ~ 166 x 10-9

Reyn.

Using this relative viscosity, Figure 9 shows that the predicted

load carrying capacity would rise from 142N to 495 N.

Figure 9 Impact of particulate/powder and gas mixture

viscosity on load capacity

Test Rig for Sub-Ambient Testing In order to assess the impact of ambient pressure on

bearing performance, a test rig, as shown in Figure 10, was

Test Data Ref (Vand)

20

18

16

14

12

10

8

6

4

2

00 10 20 30 40 50 60

Solids Fraction (φ,%) 15-003

Viscostiy of Mixture[Ref. Vand, 1948]


used. This rig concept was designed to allow us to verify the

ability of the foil bearing to operate reliably at low ambient

pressures. Tests were conducted under an array of ambient

pressure conditions. The entire test rig was made to fit inside a

simple cylindrical vacuum chamber with an outer diameter and

length of 406 X 914 mm (16 by 36 inches), respectively. The

rotor system for this testing was limited to 30,000 rpm since the

228.9 mm (9-inch) simulated subscale flywheel disc was a

safety margin of approximately 2 was used to limit the high

speed bore stresses. Total rotor weight was 11.9 kgf (116.7N)

and length was 700 mm. Each of the four journal bearings was

36.5 mm in diameter and 30 mm in length. Axial position was

controlled with the 91.5 mm diameter thrust foil bearing

located on the motor. A safety containment partial arc thrust

bearing with loose clearance was installed on the 228.9 mm

central test disc.

Figure 10 Cross Section View of a Chamber and Modular

Flywheel Simulator with Motor/Generator

The vacuum chamber hardware, shown in Figure 10, was

fabricated, and preliminary tests of the vacuum pump and test

chamber were completed. Using our Welch Model 1397

DuoSeal vacuum pump, testing to verify the ability to pump the

chamber down to at least 6.8 kPa (1 psia) was conducted. This

vacuum level was achieved after operating the vacuum pump

for approximately 1 minute. After approximately 1 hour, the

vacuum level was checked again and found to have remained

the same. Figure 11 shows the assembled rotor system being

installed into the vacuum chamber.

The purpose of building the rotor and vacuum chamber

was to conduct coast down tests with the modular design to

assess potential bearing performance and windage losses for an

entire simulated flywheel rotor system on foil bearings under

different ambient pressure conditions. The preliminary test

plan called for spinning the entire assembly to approximately

30,000 rpm and then shutting off the asynchronous/induction

motor. Coast down times from top speed to approximately

touchdown (contact between rotor and foil bearing) were

measured. Following testing at ambient pressure conditions, a

series of tests at sequentially lower absolute pressures was

conducted to determine the minimum ambient condition

permissible for the bearing system being used. For each test,

the method was to bring the rotor to full speed of 30,000 rpm,

draw down the vacuum to a specified test level, cut power to

the motor, and record coast down time and speed. An induction

motor was used for these tests to mitigate the influence of

electromagnetic fields on coast down.

Figure 11 Assembled Flywheel and Motor/Generator

being Installed in the Vacuum Chamber

Figure 12 and Figure 13 present results for the coastdown

tests at ambient pressure conditions from 101.4 kPa (14.7 psia)

to 7.6 kPa (1.1 psia). Figure 12 shows that as ambient pressure

is decreased, the windage losses also decrease since the time

required to touchdown continually increases. Of particular note

is the difference seen between the last two tests at 16.5 kPa (2.4

psia) and 7.6 kPa (1.1 psia) of ambient pressure. At the

beginning of the unpowered coastdown, the deceleration rate

for the 7.6 kPa ambient condition is much less than all other

tests. However, midway through the coast down, the

deceleration rate for the 7.6 kPa condition changes, resulting in

a faster total time to zero rpm than for the 16.5 kPa condition.

This test shows that at the lowest ambient pressure test

condition, the transition from windage loss to a combination of

bearing power loss and light friction between the shaft and

bearing occurs at a relatively high speed and, thereafter,

dominates the deceleration. At the lowest ambient pressure

condition, the thickness of the bearing gas film is so thin that it

is on the same order as the surface finish, which results in

partial contact between the bearing and the shaft. The

increased drag, therefore, increases the deceleration rate. While

this is true for the 7.6 kPa condition, it is evident that at the

16.5 kPa condition, good separation between rotor and bearing

exists to permit a very long coast down with minimal losses due

to the bearings and rotor windage. Reviewing the deceleration

rates, as shown in Figure 13, supports the contention that the

power loss at 16.5 kPa remains dominated by windage as

opposed to the foil bearings since there is no evidence of a

change in deceleration rates, even near the end of the cycle.

Besides assessing coastdown times, Figure 14 shows motor

power needed to maintain full speed under various ambient

chamber pressures. Power loss decreases to approximately 700

watts when operating at approximately 7.6 kPa.


Of special note is the case at 7.6 kPa during coast down as

speed approached approximately 20,000 rpm, the rate of

change in speed increases, as seen in Figure 12 and Figure 13.

This region is expanded for a better comparison of deceleration

and torque in Figure 15. In the initial region, torque remains

fairly constant from a speed of 25,000 to 21,000 rpm at which

point torque begins to increase and speed decreases more

quickly. However, once torque peaks at approximately 19,000

rpm (Region 1), there is a sudden drop in torque and a

corresponding decrease in the deceleration or rate of speed

change (Region2). This is followed by another gradual increase

in torque (Region 3), and a less dramatic drop in torque as

speed decreases to approximately 12,000 rpm (Region 4).

Below 11,000 rpm torque rises quickly and rotor touchdown

occurs. It is postulated that the generation of powder resulted

from the intermittent contact between rotor and the CSFB

Korolon® coating and, correspondingly, produced a gas/powder

mixture with viscosity that higher than air and which was

sufficient to increase bearing load carrying capacity to sustain

operation. It is further postulated that as speed continued to

decrease and load capacity reduced even more, additional

intermittent rubs again occurred to generate more debris which

in turn increased viscosity thereby increasing load capacity at a

slightly higher torque. Thus, the premise is made that both

hydrodynamic and morphological effects were actively

involved in maintaining rotor levitation at the low ambient

pressure. Foil bearing temperature was also monitored during

each subambient pressure test to verify that hydrodynamic

action was indeed present. As seen in Figure 16, bearing

temperature rise during the course of the test was limited to

only 10°C. If extensive rubbing, such as would be expected in

a boundary lubrication regime were to be experienced much

higher temperature rise should have been experienced. Thus

the presence of the third body lubricious particulates combined

with the limited gas molecules appears to be providing the

media producing hydrodynamic lift.

Figure 15 Torque and coastdown time versus speed

2D Graph 1

Speed (rpm)

80001000012000140001600018000200002200024000

To

rqu

e (

N-m

)

0.0

0.2

0.4

0.6

0.8

1.0

Co

astd

ow

n T

ime

(se

c)

200

250

300

350

400

450

500

-13.6 Psig velocity vs N-m at 1.1

-13.6 Psig vs Time

1 2 3 4

Torque

Time

Figure 12 Summary of coastdown tests at ambient pressures to 7.6 kPa (1.1 psia).

Figure 13 Deceleration Rates for Different Ambient Pressure Conditions Time Synchronized to Ending Condition

Figure 14 Motor power for required to operate the flywheel at 30,000 rpm as a function of ambient pressure

Time (sec)

200 300 400 500

Speed

(rp

m)

0

5000

10000

15000

20000

25000

30000

101.3 kPa (14.7 Psig )

87.6 kPa (12.7 Psig)

67 kPa (9.7 Psig )

32.4 kPa (4.7 Psig)

16.5 kPa (2.4 Psig)

7.6 kPa (1.1 Psig)

Measured Power Loss vs Ambient Pressure at 30,000 rpm

Chamber Pressure (kPa)

0 20 40 60 80 100 120

Pow

er

Loss (

watt

s)

0

1000

2000

3000

4000


Figure 16 Variation in bearing temperature during low ambient pressure coast down test

Flywheel Test Rig for Full Scale Testing Figure 17 and Figure 18 show the test facility used to

demonstrate operation of a 925 N flywheel simulator rotor

supported on foil gas bearings and the circulating thermal

management flow path through the system. Each 76 mm

diameter by 102 mm long bearing had approximately 463 N

static load during testing. Initial dynamic testing has been

completed to the design speed of 40,000 rpm in both air and

with low density helium gas. To verify thermal stability,

operation was first conducted in air and then with helium gas to

speeds of 28,500 rpm. Figure 19 presents result of testing to

28,500 rpm and shows bearing temperatures in air and helium.

At speed to 20,000 rpm air was used for thermal management

showing a maximum temperature of approximately 66C (150F)

for the rotor non-driven end (NDE) of the rotor for an ambient

pressure condition of 101.4 kPa (14.7 psia). At that speed

circulating helium replaced the air the initial temperature spike

was caused by the switching from air to helium and the

corresponding disruption in gas flow through the system.

Temperature continued to increase slightly with increasing

speed until 28,500 rpm was reached with two incremental

increases in helium flow through the system. Helium was

selected both for its heat capacity and low density which would

aid in thermal management and to cut down windage losses on

the large FESS rotor. While bearing temperatures did climb

during the test, it should be noted that maximum temperature

did not exceed 90 C and would not have been expected to

exceed about 100 C.

Figure 17 Flywheel energy storage test system with 925 N rotor

Figure 18 Thermal management circulating helium gas flow path

Figure 19 Preliminary testing to 28,500 rpm showing bearing temperatures with helium gas for thermal management

Figure 20 Test runs using different cooling flows showing repeatability of response

Figure 21 Flywheel response at end connected to motor/generator

Figure 20 and Figure 21 show that rotor response was

repeatable during acceleration and deceleration. In addition to

verifying repeatability this testing was used to compare the

Coastdown from 30,000 rpm at 7.6 kPa Ambient Pressure

Time

0 100 200 300 400 500

Speed (

rpm

)

0

5000

10000

15000

20000

25000

30000

Tem

pera

ture

(C

)

25

30

35

40

45

Speed

Temperature

Test with He Gas

TIME

15:04:00 15:19:00 15:34:00 15:49:00 16:04:00 16:19:00 16:34:00

BE

AR

ING

TE

MP

ER

AT

UR

E

50

75

100

125

150

175

200

225

SP

EE

D (

KR

PM

)

0

5

10

15

20

25

30

Pre

ssu

re (

kP

a)

0

20

40

60

80

100 T2 NDE BDC DOWNSTREAM

T4 NDE BDC UPSTREAM

T10 DE BDC UPSTREAM

T12 DE BDC DOWNSTREAM

SPEED

Pressure (kPa)

22 SCFM He

32 scfm He

38 scfm He29 scfm He

Air

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000

Mag

nitu

de (m

ils)

Frequency (RPM)

FLYWHEEL - FREE END RESPONSE (VERT)

RUN-UP (10 SCFM)

RUN-UP2 (10 SCFM)

COAST-DOWN (18 SCFM)


6975 rpm

7390 rpm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000

Mag

nitu

de (m

ils)

Frequency (RPM)

FLYWHEEL COUPLING END RESPONSE (VERT)

RUN-UP (10 SCFM)

RUN-UP2 (10 SCFM)



6975 rpm

7388 rpm

8138 rpm


predicted and measured rigid body critical speed. The

predicted flywheel cylindrical mode critical speed shown in

Figure 22 occurs at approximately 6975 rpm, which compares

very favorably with the measured response.

Figure 22 Predicted system critical speed at 6900 rpm and corresponding mode shape

Following the preliminary testing, operation to full speed

of 40,000 rpm was conducted with helium gas in the flywheel

chamber. As seen in Figure 23 full speed of 40,000 rpm was

achieved with very low vibrations, with maximum peak

synchronous vibration being less than 10 micron. It should also

be noted that the total vibration signature across all frequencies

of interest are very small, which is indicative of a stable system

with good bearing damping. Bearing temperatures presented in

Figure 24 show that for approximately 0.45 kg/min helium gas

flow, maximum bearing temperature did not exceed 82C (180F)

and that the differential bearing temperature across the axial

length of the bearing (102 mm length) was only about 22C

(40F). Similarly, the foil bearing near the coupling and

motor/generator maintained low temperatures and an axial

gradient of approximately 27C. These small axial thermal

gradient are indicative of a bearing thermal environment that is

managed very well, especially given the large load being

carried by each bearing.

Figure 23 Instantaneous FFT while operating at 40,000 rpm

Figure 24 Foil bearing temperatures during operation to 40 krpm with helium cool gas

CONCLUSIONS In this paper the authors have shown the ability of

advanced 5th

generation compliant foil bearings to support large

flywheel rotors weighing in excess of 920 N and which can

operate to speeds in excess of 40,000 rpm. The dynamic testing

of the simulated flywheel energy storage system showed

excellent correlation between predicted critical speed and

measured response. The correlation between actual rotor

response and critical speed predictions give confidence and

validate both the rotor model and foil bearing design analysis

that was used to predict the dynamic coefficients.

Through a second rotor test system, testing was conducted

at pressures as low as 7 kPa to demonstrate the ability of foil

bearings to operate in low ambient pressures consistent with

flywheel energy storage system needs for low windage loss.

The authors also presented a hypothesis and the mechanisms

involved in a hydrodynamic phenomenon that allows a foil

bearing to operate successfully when the mean free path of the

air molecules is exceedingly large due to low ambient

pressures.

This successful conclusion of this combined series of tests

and the correlation achieved provide a basis for future

consideration of foil bearings and their use with large rotor

systems and even those operating at low ambient pressures.

NOMENCLATURE CSFB Compliant Surface Foil Bearing

C Clearance

e Eccentricity

E Young’s Modulus

ht Altitude (m)

HN Nominal Minimum Film thickness

hmin Minimum Film thickness

h gap = R2-R1

L Length [m]

R Radius [m]

Re Reynolds No. = ρ R1 ω h / μ

W Shaft Load [kg]

Λ Bearing Parameter

ρ Density [kg/m3]

ω Rotational Speed [rad/s]

T7R2 COUPLED SYSTEMFW JOURNAL BEARING TEMPS

40 SCFM(He) FLYWHEEL COOLING

TIME

11:08:00 11:18:00 11:28:00 11:38:00

BE

AR

ING

TE

MP

ER

AT

UR

E (

F)

60

80

100

120

140

160

180

200

SP

EE

D (

KR

PM

)

0

5

10

15

20

25

30

35

40

FREE END FLYWHEEL (DWN STREAM)

T10 DE BDC UPSTREAM COOLING

T12 DE BDC DOWNSTREAM COOLING

SPEED

T4 JRNL NDE BDC IN

SpeedFree-End Brg Temp (exit)

Free-End BrgTemp (in)

Coupled-End Brg Temp (in)

Coupled-End Brg Temp (exit)


μ Dynamic viscosity [Pa-s]

υ Kinematic viscosity [m2/s]

Ta Taylor Number = [R1ωh/υ]√(h/R1)

ACKNOWLEDGMENTS The authors would like to thank the both MiTi and the U.S.

Navy for their support of this effort.

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